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<!--XBRL Document Created with Wdesk from Workiva-->
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    <link:label id="lab_us-gaap_DisposalGroupIncludingDiscontinuedOperationAccountsNotesAndLoansReceivableNet_label_en-US" xlink:label="lab_us-gaap_DisposalGroupIncludingDiscontinuedOperationAccountsNotesAndLoansReceivableNet" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Disposal Group, Including Discontinued Operation, Accounts, Notes and Loans Receivable, Net</link:label>
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    <link:label id="lab_us-gaap_BusinessCombinationAcquisitionRelatedCosts_label_en-US" xlink:label="lab_us-gaap_BusinessCombinationAcquisitionRelatedCosts" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Business Combination, Acquisition Related Costs</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_BusinessCombinationAcquisitionRelatedCosts" xlink:href="https://xbrl.fasb.org/us-gaap/2021/elts/us-gaap-2021-01-31.xsd#us-gaap_BusinessCombinationAcquisitionRelatedCosts"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_BusinessCombinationAcquisitionRelatedCosts" xlink:to="lab_us-gaap_BusinessCombinationAcquisitionRelatedCosts" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DisposalGroupIncludingDiscontinuedOperationOtherCurrentLiabilities_60a82b68-6554-433f-9088-7bd3f383ba77_terseLabel_en-US" xlink:label="lab_us-gaap_DisposalGroupIncludingDiscontinuedOperationOtherCurrentLiabilities" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Disposal Group, Including Discontinued Operation, Other Liabilities, Current</link:label>
    <link:label id="lab_us-gaap_DisposalGroupIncludingDiscontinuedOperationOtherCurrentLiabilities_label_en-US" xlink:label="lab_us-gaap_DisposalGroupIncludingDiscontinuedOperationOtherCurrentLiabilities" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Disposal Group, Including Discontinued Operation, Other Liabilities, Current</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DisposalGroupIncludingDiscontinuedOperationOtherCurrentLiabilities" xlink:href="https://xbrl.fasb.org/us-gaap/2021/elts/us-gaap-2021-01-31.xsd#us-gaap_DisposalGroupIncludingDiscontinuedOperationOtherCurrentLiabilities"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DisposalGroupIncludingDiscontinuedOperationOtherCurrentLiabilities" xlink:to="lab_us-gaap_DisposalGroupIncludingDiscontinuedOperationOtherCurrentLiabilities" xlink:type="arc" order="1"/>
    <link:label id="lab_codi_DistributionExpensePreferredShareholders_d0d1a366-cfb2-48a8-a55e-a6e5efb9e813_terseLabel_en-US" xlink:label="lab_codi_DistributionExpensePreferredShareholders" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Distribution Expense, Preferred Shareholders</link:label>
    <link:label id="lab_codi_DistributionExpensePreferredShareholders_label_en-US" xlink:label="lab_codi_DistributionExpensePreferredShareholders" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Distribution Expense, Preferred Shareholders</link:label>
    <link:label id="lab_codi_DistributionExpensePreferredShareholders_documentation_en-US" xlink:label="lab_codi_DistributionExpensePreferredShareholders" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Distribution Expense, Preferred Shareholders</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_codi_DistributionExpensePreferredShareholders" xlink:href="codi-20220331.xsd#codi_DistributionExpensePreferredShareholders"/>
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    <link:label id="lab_dei_SecurityExchangeName_39f5b327-01af-4c2e-b43b-2fa827b3fead_terseLabel_en-US" xlink:label="lab_dei_SecurityExchangeName" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Security Exchange Name</link:label>
    <link:label id="lab_dei_SecurityExchangeName_label_en-US" xlink:label="lab_dei_SecurityExchangeName" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Security Exchange Name</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_SecurityExchangeName" xlink:href="https://xbrl.sec.gov/dei/2021q4/dei-2021q4.xsd#dei_SecurityExchangeName"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_SecurityExchangeName" xlink:to="lab_dei_SecurityExchangeName" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_EntityIncorporationStateCountryCode_1ee7f0f2-0d76-4e9d-8bbb-4ae32665875f_terseLabel_en-US" xlink:label="lab_dei_EntityIncorporationStateCountryCode" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Entity Incorporation, State or Country Code</link:label>
    <link:label id="lab_dei_EntityIncorporationStateCountryCode_label_en-US" xlink:label="lab_dei_EntityIncorporationStateCountryCode" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Entity Incorporation, State or Country Code</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_EntityIncorporationStateCountryCode" xlink:href="https://xbrl.sec.gov/dei/2021q4/dei-2021q4.xsd#dei_EntityIncorporationStateCountryCode"/>
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    <link:label id="lab_us-gaap_RevenueFromContractWithCustomerAbstract_b6ba7b8d-8eac-4898-9c7c-1a6ecd62138c_terseLabel_en-US" xlink:label="lab_us-gaap_RevenueFromContractWithCustomerAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Revenue from Contract with Customer [Abstract]</link:label>
    <link:label id="lab_us-gaap_RevenueFromContractWithCustomerAbstract_label_en-US" xlink:label="lab_us-gaap_RevenueFromContractWithCustomerAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Revenue from Contract with Customer [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_RevenueFromContractWithCustomerAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2021/elts/us-gaap-2021-01-31.xsd#us-gaap_RevenueFromContractWithCustomerAbstract"/>
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    <link:label id="lab_codi_AltorMember_f1c10592-29ea-42bb-8764-e7b380c3adf0_terseLabel_en-US" xlink:label="lab_codi_AltorMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Altor</link:label>
    <link:label id="lab_codi_AltorMember_label_en-US" xlink:label="lab_codi_AltorMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Altor [Member]</link:label>
    <link:label id="lab_codi_AltorMember_documentation_en-US" xlink:label="lab_codi_AltorMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Altor</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_codi_AltorMember" xlink:href="codi-20220331.xsd#codi_AltorMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_codi_AltorMember" xlink:to="lab_codi_AltorMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_OperatingLeaseWeightedAverageRemainingLeaseTerm1_3ff17824-ac8c-47bb-89ad-41921a03ae05_terseLabel_en-US" xlink:label="lab_us-gaap_OperatingLeaseWeightedAverageRemainingLeaseTerm1" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Weighted-average remaining lease term (years)</link:label>
    <link:label id="lab_us-gaap_OperatingLeaseWeightedAverageRemainingLeaseTerm1_label_en-US" xlink:label="lab_us-gaap_OperatingLeaseWeightedAverageRemainingLeaseTerm1" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Operating Lease, Weighted Average Remaining Lease Term</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OperatingLeaseWeightedAverageRemainingLeaseTerm1" xlink:href="https://xbrl.fasb.org/us-gaap/2021/elts/us-gaap-2021-01-31.xsd#us-gaap_OperatingLeaseWeightedAverageRemainingLeaseTerm1"/>
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    <link:label id="lab_us-gaap_OtherAssetsNoncurrent_34866e6f-c8dc-4d67-95e1-4a5c1afcb0ef_terseLabel_en-US" xlink:label="lab_us-gaap_OtherAssetsNoncurrent" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Other non-current assets</link:label>
    <link:label id="lab_us-gaap_OtherAssetsNoncurrent_label_en-US" xlink:label="lab_us-gaap_OtherAssetsNoncurrent" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Other Assets, Noncurrent</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OtherAssetsNoncurrent" xlink:href="https://xbrl.fasb.org/us-gaap/2021/elts/us-gaap-2021-01-31.xsd#us-gaap_OtherAssetsNoncurrent"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_OtherAssetsNoncurrent" xlink:to="lab_us-gaap_OtherAssetsNoncurrent" xlink:type="arc" order="1"/>
    <link:label id="lab_srt_ScheduleOfEquityMethodInvestmentEquityMethodInvesteeNameAxis_68522925-1500-41d0-8f38-d9777e1313d5_terseLabel_en-US" xlink:label="lab_srt_ScheduleOfEquityMethodInvestmentEquityMethodInvesteeNameAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Investment, Name [Axis]</link:label>
    <link:label id="lab_srt_ScheduleOfEquityMethodInvestmentEquityMethodInvesteeNameAxis_label_en-US" xlink:label="lab_srt_ScheduleOfEquityMethodInvestmentEquityMethodInvesteeNameAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Investment, Name [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_srt_ScheduleOfEquityMethodInvestmentEquityMethodInvesteeNameAxis" xlink:href="https://xbrl.fasb.org/srt/2021/elts/srt-2021-01-31.xsd#srt_ScheduleOfEquityMethodInvestmentEquityMethodInvesteeNameAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_srt_ScheduleOfEquityMethodInvestmentEquityMethodInvesteeNameAxis" xlink:to="lab_srt_ScheduleOfEquityMethodInvestmentEquityMethodInvesteeNameAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_codi_OwnershipPercentageOfNoncontrollingShareholders_cadfcdba-29da-43b7-aad5-6c9713f5e2d6_terseLabel_en-US" xlink:label="lab_codi_OwnershipPercentageOfNoncontrollingShareholders" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">% Ownership</link:label>
    <link:label id="lab_codi_OwnershipPercentageOfNoncontrollingShareholders_label_en-US" xlink:label="lab_codi_OwnershipPercentageOfNoncontrollingShareholders" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Ownership Percentage Of Noncontrolling Shareholders</link:label>
    <link:label id="lab_codi_OwnershipPercentageOfNoncontrollingShareholders_documentation_en-US" xlink:label="lab_codi_OwnershipPercentageOfNoncontrollingShareholders" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Ownership percentage of noncontrolling shareholders.</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_codi_OwnershipPercentageOfNoncontrollingShareholders" xlink:href="codi-20220331.xsd#codi_OwnershipPercentageOfNoncontrollingShareholders"/>
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    <link:label id="lab_us-gaap_DefinedBenefitPlanExpectedReturnOnPlanAssets_9d1e9f2a-ed25-45c3-8ba4-3bbe078bd41b_negatedLabel_en-US" xlink:label="lab_us-gaap_DefinedBenefitPlanExpectedReturnOnPlanAssets" xlink:role="http://www.xbrl.org/2009/role/negatedLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Expected return on plan assets</link:label>
    <link:label id="lab_us-gaap_DefinedBenefitPlanExpectedReturnOnPlanAssets_label_en-US" xlink:label="lab_us-gaap_DefinedBenefitPlanExpectedReturnOnPlanAssets" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Defined Benefit Plan, Expected Return (Loss) on Plan Assets</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DefinedBenefitPlanExpectedReturnOnPlanAssets" xlink:href="https://xbrl.fasb.org/us-gaap/2021/elts/us-gaap-2021-01-31.xsd#us-gaap_DefinedBenefitPlanExpectedReturnOnPlanAssets"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DefinedBenefitPlanExpectedReturnOnPlanAssets" xlink:to="lab_us-gaap_DefinedBenefitPlanExpectedReturnOnPlanAssets" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ProceedsFromMinorityShareholders_8a9c2772-06e8-449d-aa03-46c4224fc202_terseLabel_en-US" xlink:label="lab_us-gaap_ProceedsFromMinorityShareholders" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Net proceeds provided by noncontrolling shareholders</link:label>
    <link:label id="lab_us-gaap_ProceedsFromMinorityShareholders_label_en-US" xlink:label="lab_us-gaap_ProceedsFromMinorityShareholders" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Proceeds from Noncontrolling Interests</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ProceedsFromMinorityShareholders" xlink:href="https://xbrl.fasb.org/us-gaap/2021/elts/us-gaap-2021-01-31.xsd#us-gaap_ProceedsFromMinorityShareholders"/>
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    <link:label id="lab_us-gaap_StatementBusinessSegmentsAxis_b0258318-cdfc-4160-bb73-adff8f3c9221_terseLabel_en-US" xlink:label="lab_us-gaap_StatementBusinessSegmentsAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Segments [Axis]</link:label>
    <link:label id="lab_us-gaap_StatementBusinessSegmentsAxis_label_en-US" xlink:label="lab_us-gaap_StatementBusinessSegmentsAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Segments [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_StatementBusinessSegmentsAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2021/elts/us-gaap-2021-01-31.xsd#us-gaap_StatementBusinessSegmentsAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_StatementBusinessSegmentsAxis" xlink:to="lab_us-gaap_StatementBusinessSegmentsAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_CompensationAndRetirementDisclosureAbstract_faf6ae50-fbd4-48d0-bb8b-8f772aac771f_terseLabel_en-US" xlink:label="lab_us-gaap_CompensationAndRetirementDisclosureAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Retirement Benefits [Abstract]</link:label>
    <link:label id="lab_us-gaap_CompensationAndRetirementDisclosureAbstract_label_en-US" xlink:label="lab_us-gaap_CompensationAndRetirementDisclosureAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Retirement Benefits [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CompensationAndRetirementDisclosureAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2021/elts/us-gaap-2021-01-31.xsd#us-gaap_CompensationAndRetirementDisclosureAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_CompensationAndRetirementDisclosureAbstract" xlink:to="lab_us-gaap_CompensationAndRetirementDisclosureAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalentsPeriodIncreaseDecreaseIncludingExchangeRateEffect_1aa6597b-1ff3-40a7-816e-fd730b1a5ffc_totalLabel_en-US" xlink:label="lab_us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalentsPeriodIncreaseDecreaseIncludingExchangeRateEffect" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Net decrease in cash and cash equivalents</link:label>
    <link:label id="lab_us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalentsPeriodIncreaseDecreaseIncludingExchangeRateEffect_label_en-US" xlink:label="lab_us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalentsPeriodIncreaseDecreaseIncludingExchangeRateEffect" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Cash, Cash Equivalents, Restricted Cash and Restricted Cash Equivalents, Period Increase (Decrease), Including Exchange Rate Effect</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalentsPeriodIncreaseDecreaseIncludingExchangeRateEffect" xlink:href="https://xbrl.fasb.org/us-gaap/2021/elts/us-gaap-2021-01-31.xsd#us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalentsPeriodIncreaseDecreaseIncludingExchangeRateEffect"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalentsPeriodIncreaseDecreaseIncludingExchangeRateEffect" xlink:to="lab_us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalentsPeriodIncreaseDecreaseIncludingExchangeRateEffect" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AcquiredFiniteLivedIntangibleAssetsLineItems_75522968-fdb4-462b-bd80-1f7814399d84_terseLabel_en-US" xlink:label="lab_us-gaap_AcquiredFiniteLivedIntangibleAssetsLineItems" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Acquired Finite-Lived Intangible Assets [Line Items]</link:label>
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    <link:label id="lab_us-gaap_IncomeLossFromContinuingOperations_e1bd2992-1e5f-4b9a-9219-86472eb10b2a_terseLabel_en-US" xlink:label="lab_us-gaap_IncomeLossFromContinuingOperations" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Income from continuing operations</link:label>
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    <link:label id="lab_us-gaap_CommonStockValue_722ba8c0-9fe8-44e7-9d87-255089c2e524_verboseLabel_en-US" xlink:label="lab_us-gaap_CommonStockValue" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Trust common shares, no par value, 500,000 authorized; 69,450 shares issued and outstanding at March 31, 2022 and 68,738 issued and outstanding at December 31, 2021</link:label>
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    <link:label id="lab_us-gaap_GoodwillAcquiredDuringPeriod_36d6493a-16bd-4446-87d8-88bdb6f2b363_terseLabel_en-US" xlink:label="lab_us-gaap_GoodwillAcquiredDuringPeriod" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Goodwill, Acquired During Period</link:label>
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    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_GoodwillAcquiredDuringPeriod" xlink:href="https://xbrl.fasb.org/us-gaap/2021/elts/us-gaap-2021-01-31.xsd#us-gaap_GoodwillAcquiredDuringPeriod"/>
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    <link:label id="lab_us-gaap_LesseeOperatingLeaseLiabilityPaymentsRemainderOfFiscalYear_7ae308b4-43eb-44b8-bfec-9461cbc3134d_terseLabel_en-US" xlink:label="lab_us-gaap_LesseeOperatingLeaseLiabilityPaymentsRemainderOfFiscalYear" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">2019</link:label>
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    <link:label id="lab_codi_VelocityOutdoorMember_3a10a455-1e41-4d0c-94ca-912ff4a6153e_terseLabel_en-US" xlink:label="lab_codi_VelocityOutdoorMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Velocity</link:label>
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    <link:label id="lab_us-gaap_Depreciation_496fb23d-f44f-4f0b-a8fc-aa0533d654ac_terseLabel_en-US" xlink:label="lab_us-gaap_Depreciation" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Depreciation expense</link:label>
    <link:label id="lab_us-gaap_Depreciation_label_en-US" xlink:label="lab_us-gaap_Depreciation" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Depreciation</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_Depreciation" xlink:href="https://xbrl.fasb.org/us-gaap/2021/elts/us-gaap-2021-01-31.xsd#us-gaap_Depreciation"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_Depreciation" xlink:to="lab_us-gaap_Depreciation" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_IncomeLossFromDiscontinuedOperationsNetOfTaxAttributableToNoncontrollingInterest_bbe88655-98f9-469e-8e5d-8549f79ad14f_terseLabel_en-US" xlink:label="lab_us-gaap_IncomeLossFromDiscontinuedOperationsNetOfTaxAttributableToNoncontrollingInterest" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Less: Net income from discontinued operations attributable to noncontrolling interest</link:label>
    <link:label id="lab_us-gaap_IncomeLossFromDiscontinuedOperationsNetOfTaxAttributableToNoncontrollingInterest_label_en-US" xlink:label="lab_us-gaap_IncomeLossFromDiscontinuedOperationsNetOfTaxAttributableToNoncontrollingInterest" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Income (Loss) from Discontinued Operations, Net of Tax, Attributable to Noncontrolling Interest</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_IncomeLossFromDiscontinuedOperationsNetOfTaxAttributableToNoncontrollingInterest" xlink:href="https://xbrl.fasb.org/us-gaap/2021/elts/us-gaap-2021-01-31.xsd#us-gaap_IncomeLossFromDiscontinuedOperationsNetOfTaxAttributableToNoncontrollingInterest"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_IncomeLossFromDiscontinuedOperationsNetOfTaxAttributableToNoncontrollingInterest" xlink:to="lab_us-gaap_IncomeLossFromDiscontinuedOperationsNetOfTaxAttributableToNoncontrollingInterest" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LongtermDebtTypeDomain_9a4a1027-1f2b-43de-8891-84d256a35ecf_terseLabel_en-US" xlink:label="lab_us-gaap_LongtermDebtTypeDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Long-term Debt, Type [Domain]</link:label>
    <link:label id="lab_us-gaap_LongtermDebtTypeDomain_label_en-US" xlink:label="lab_us-gaap_LongtermDebtTypeDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Long-term Debt, Type [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LongtermDebtTypeDomain" xlink:href="https://xbrl.fasb.org/us-gaap/2021/elts/us-gaap-2021-01-31.xsd#us-gaap_LongtermDebtTypeDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LongtermDebtTypeDomain" xlink:to="lab_us-gaap_LongtermDebtTypeDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_EffectOfExchangeRateOnCashCashEquivalentsRestrictedCashAndRestrictedCashEquivalentsIncludingDisposalGroupAndDiscontinuedOperations_169b7bbe-9ef3-486b-a1d5-8def40a5b3bd_terseLabel_en-US" xlink:label="lab_us-gaap_EffectOfExchangeRateOnCashCashEquivalentsRestrictedCashAndRestrictedCashEquivalentsIncludingDisposalGroupAndDiscontinuedOperations" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Foreign currency impact on cash</link:label>
    <link:label id="lab_us-gaap_EffectOfExchangeRateOnCashCashEquivalentsRestrictedCashAndRestrictedCashEquivalentsIncludingDisposalGroupAndDiscontinuedOperations_label_en-US" xlink:label="lab_us-gaap_EffectOfExchangeRateOnCashCashEquivalentsRestrictedCashAndRestrictedCashEquivalentsIncludingDisposalGroupAndDiscontinuedOperations" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Effect of Exchange Rate on Cash, Cash Equivalents, Restricted Cash and Restricted Cash Equivalents, Including Disposal Group and Discontinued Operations</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_EffectOfExchangeRateOnCashCashEquivalentsRestrictedCashAndRestrictedCashEquivalentsIncludingDisposalGroupAndDiscontinuedOperations" xlink:href="https://xbrl.fasb.org/us-gaap/2021/elts/us-gaap-2021-01-31.xsd#us-gaap_EffectOfExchangeRateOnCashCashEquivalentsRestrictedCashAndRestrictedCashEquivalentsIncludingDisposalGroupAndDiscontinuedOperations"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_EffectOfExchangeRateOnCashCashEquivalentsRestrictedCashAndRestrictedCashEquivalentsIncludingDisposalGroupAndDiscontinuedOperations" xlink:to="lab_us-gaap_EffectOfExchangeRateOnCashCashEquivalentsRestrictedCashAndRestrictedCashEquivalentsIncludingDisposalGroupAndDiscontinuedOperations" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_PreferredStockLiquidationPreference_c13e7901-3895-4164-8813-b124c41be657_terseLabel_en-US" xlink:label="lab_us-gaap_PreferredStockLiquidationPreference" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Preferred Stock, Liquidation Preference Per Share</link:label>
    <link:label id="lab_us-gaap_PreferredStockLiquidationPreference_label_en-US" xlink:label="lab_us-gaap_PreferredStockLiquidationPreference" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Preferred Stock, Liquidation Preference Per Share</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PreferredStockLiquidationPreference" xlink:href="https://xbrl.fasb.org/us-gaap/2021/elts/us-gaap-2021-01-31.xsd#us-gaap_PreferredStockLiquidationPreference"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_PreferredStockLiquidationPreference" xlink:to="lab_us-gaap_PreferredStockLiquidationPreference" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ScheduleOfProductWarrantyLiabilityTableTextBlock_c0961ca6-7463-4def-8d5d-84942ac37016_terseLabel_en-US" xlink:label="lab_us-gaap_ScheduleOfProductWarrantyLiabilityTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Change in Carrying Value of Company's Warranty Liability</link:label>
    <link:label id="lab_us-gaap_ScheduleOfProductWarrantyLiabilityTableTextBlock_label_en-US" xlink:label="lab_us-gaap_ScheduleOfProductWarrantyLiabilityTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Schedule of Product Warranty Liability [Table Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ScheduleOfProductWarrantyLiabilityTableTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2021/elts/us-gaap-2021-01-31.xsd#us-gaap_ScheduleOfProductWarrantyLiabilityTableTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ScheduleOfProductWarrantyLiabilityTableTextBlock" xlink:to="lab_us-gaap_ScheduleOfProductWarrantyLiabilityTableTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_codi_Debtissuanceaggregateprincipalamount_9b980972-1d97-4baa-93c8-33917cbebee5_terseLabel_en-US" xlink:label="lab_codi_Debtissuanceaggregateprincipalamount" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Debt issuance, aggregate principal amount</link:label>
    <link:label id="lab_codi_Debtissuanceaggregateprincipalamount_label_en-US" xlink:label="lab_codi_Debtissuanceaggregateprincipalamount" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Debt issuance, aggregate principal amount</link:label>
    <link:label id="lab_codi_Debtissuanceaggregateprincipalamount_documentation_en-US" xlink:label="lab_codi_Debtissuanceaggregateprincipalamount" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Debt issuance, aggregate principal amount</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_codi_Debtissuanceaggregateprincipalamount" xlink:href="codi-20220331.xsd#codi_Debtissuanceaggregateprincipalamount"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_codi_Debtissuanceaggregateprincipalamount" xlink:to="lab_codi_Debtissuanceaggregateprincipalamount" xlink:type="arc" order="1"/>
    <link:label id="lab_codi_GoodwillImpairmentTestingFairValueExceedingCarryingValuePercent_d260fce3-a783-4f7c-96a1-bbfe54cbcf11_terseLabel_en-US" xlink:label="lab_codi_GoodwillImpairmentTestingFairValueExceedingCarryingValuePercent" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Goodwill Impairment Testing, Fair Value Exceeding Carrying Value, Percent</link:label>
    <link:label id="lab_codi_GoodwillImpairmentTestingFairValueExceedingCarryingValuePercent_label_en-US" xlink:label="lab_codi_GoodwillImpairmentTestingFairValueExceedingCarryingValuePercent" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Goodwill Impairment Testing, Fair Value Exceeding Carrying Value, Percent</link:label>
    <link:label id="lab_codi_GoodwillImpairmentTestingFairValueExceedingCarryingValuePercent_documentation_en-US" xlink:label="lab_codi_GoodwillImpairmentTestingFairValueExceedingCarryingValuePercent" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Goodwill Impairment Testing, Fair Value Exceeding Carrying Value, Percent</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_codi_GoodwillImpairmentTestingFairValueExceedingCarryingValuePercent" xlink:href="codi-20220331.xsd#codi_GoodwillImpairmentTestingFairValueExceedingCarryingValuePercent"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_codi_GoodwillImpairmentTestingFairValueExceedingCarryingValuePercent" xlink:to="lab_codi_GoodwillImpairmentTestingFairValueExceedingCarryingValuePercent" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_OperatingLeaseLiabilityCurrentStatementOfFinancialPositionExtensibleList_28d9ee80-4004-462c-8d22-2a7089772afe_terseLabel_en-US" xlink:label="lab_us-gaap_OperatingLeaseLiabilityCurrentStatementOfFinancialPositionExtensibleList" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Operating Lease, Liability, Current, Statement of Financial Position [Extensible Enumeration]</link:label>
    <link:label id="lab_us-gaap_OperatingLeaseLiabilityCurrentStatementOfFinancialPositionExtensibleList_label_en-US" xlink:label="lab_us-gaap_OperatingLeaseLiabilityCurrentStatementOfFinancialPositionExtensibleList" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Operating Lease, Liability, Current, Statement of Financial Position [Extensible Enumeration]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OperatingLeaseLiabilityCurrentStatementOfFinancialPositionExtensibleList" xlink:href="https://xbrl.fasb.org/us-gaap/2021/elts/us-gaap-2021-01-31.xsd#us-gaap_OperatingLeaseLiabilityCurrentStatementOfFinancialPositionExtensibleList"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_OperatingLeaseLiabilityCurrentStatementOfFinancialPositionExtensibleList" xlink:to="lab_us-gaap_OperatingLeaseLiabilityCurrentStatementOfFinancialPositionExtensibleList" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_OtherNonoperatingIncomeExpense_844d59b3-4454-40c5-a05e-c37b457408b1_terseLabel_en-US" xlink:label="lab_us-gaap_OtherNonoperatingIncomeExpense" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Other income (expense), net</link:label>
    <link:label id="lab_us-gaap_OtherNonoperatingIncomeExpense_699061c7-cd6e-4522-9e14-9659fc71b4f7_verboseLabel_en-US" xlink:label="lab_us-gaap_OtherNonoperatingIncomeExpense" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Other income (expense), net</link:label>
    <link:label id="lab_us-gaap_OtherNonoperatingIncomeExpense_label_en-US" xlink:label="lab_us-gaap_OtherNonoperatingIncomeExpense" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Other Nonoperating Income (Expense)</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OtherNonoperatingIncomeExpense" xlink:href="https://xbrl.fasb.org/us-gaap/2021/elts/us-gaap-2021-01-31.xsd#us-gaap_OtherNonoperatingIncomeExpense"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_OtherNonoperatingIncomeExpense" xlink:to="lab_us-gaap_OtherNonoperatingIncomeExpense" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LongTermDebtFairValue_f26112a1-cfae-4573-bf98-2d988da167bc_terseLabel_en-US" xlink:label="lab_us-gaap_LongTermDebtFairValue" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Long-term Debt, Fair Value</link:label>
    <link:label id="lab_us-gaap_LongTermDebtFairValue_label_en-US" xlink:label="lab_us-gaap_LongTermDebtFairValue" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Long-term Debt, Fair Value</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LongTermDebtFairValue" xlink:href="https://xbrl.fasb.org/us-gaap/2021/elts/us-gaap-2021-01-31.xsd#us-gaap_LongTermDebtFairValue"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LongTermDebtFairValue" xlink:to="lab_us-gaap_LongTermDebtFairValue" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ProductWarrantyAccrualPayments_b0e9e075-9fe8-43b8-b9ad-a109c568e1ce_negatedLabel_en-US" xlink:label="lab_us-gaap_ProductWarrantyAccrualPayments" xlink:role="http://www.xbrl.org/2009/role/negatedLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Fulfillment of warranty obligations</link:label>
    <link:label id="lab_us-gaap_ProductWarrantyAccrualPayments_label_en-US" xlink:label="lab_us-gaap_ProductWarrantyAccrualPayments" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Standard and Extended Product Warranty Accrual, Decrease for Payments</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ProductWarrantyAccrualPayments" xlink:href="https://xbrl.fasb.org/us-gaap/2021/elts/us-gaap-2021-01-31.xsd#us-gaap_ProductWarrantyAccrualPayments"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ProductWarrantyAccrualPayments" xlink:to="lab_us-gaap_ProductWarrantyAccrualPayments" xlink:type="arc" order="1"/>
    <link:label id="lab_codi_DisposalGroupTotalenterprisevalue_a30f4acf-ffcc-4933-bffd-6fdcec458f8f_terseLabel_en-US" xlink:label="lab_codi_DisposalGroupTotalenterprisevalue" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Disposal Group, Total enterprise value</link:label>
    <link:label id="lab_codi_DisposalGroupTotalenterprisevalue_label_en-US" xlink:label="lab_codi_DisposalGroupTotalenterprisevalue" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Disposal Group, Total enterprise value</link:label>
    <link:label id="lab_codi_DisposalGroupTotalenterprisevalue_documentation_en-US" xlink:label="lab_codi_DisposalGroupTotalenterprisevalue" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Disposal Group, Total enterprise value</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_codi_DisposalGroupTotalenterprisevalue" xlink:href="codi-20220331.xsd#codi_DisposalGroupTotalenterprisevalue"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_codi_DisposalGroupTotalenterprisevalue" xlink:to="lab_codi_DisposalGroupTotalenterprisevalue" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_PaymentsForProceedsFromOtherInvestingActivities_61be2669-6ab3-4420-9f0c-534d3ae80376_negatedLabel_en-US" xlink:label="lab_us-gaap_PaymentsForProceedsFromOtherInvestingActivities" xlink:role="http://www.xbrl.org/2009/role/negatedLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Other investing activities</link:label>
    <link:label id="lab_us-gaap_PaymentsForProceedsFromOtherInvestingActivities_label_en-US" xlink:label="lab_us-gaap_PaymentsForProceedsFromOtherInvestingActivities" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Payments for (Proceeds from) Other Investing Activities</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PaymentsForProceedsFromOtherInvestingActivities" xlink:href="https://xbrl.fasb.org/us-gaap/2021/elts/us-gaap-2021-01-31.xsd#us-gaap_PaymentsForProceedsFromOtherInvestingActivities"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_PaymentsForProceedsFromOtherInvestingActivities" xlink:to="lab_us-gaap_PaymentsForProceedsFromOtherInvestingActivities" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_PaymentsToAcquirePropertyPlantAndEquipment_567b4887-61f1-4cd6-97f4-f405c4bdb861_negatedLabel_en-US" xlink:label="lab_us-gaap_PaymentsToAcquirePropertyPlantAndEquipment" xlink:role="http://www.xbrl.org/2009/role/negatedLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Purchases of property and equipment</link:label>
    <link:label id="lab_us-gaap_PaymentsToAcquirePropertyPlantAndEquipment_label_en-US" xlink:label="lab_us-gaap_PaymentsToAcquirePropertyPlantAndEquipment" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Payments to Acquire Property, Plant, and Equipment</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PaymentsToAcquirePropertyPlantAndEquipment" xlink:href="https://xbrl.fasb.org/us-gaap/2021/elts/us-gaap-2021-01-31.xsd#us-gaap_PaymentsToAcquirePropertyPlantAndEquipment"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_PaymentsToAcquirePropertyPlantAndEquipment" xlink:to="lab_us-gaap_PaymentsToAcquirePropertyPlantAndEquipment" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_OtherLiabilitiesCurrent_93608e6d-f085-42b4-baac-9b06058d1d34_terseLabel_en-US" xlink:label="lab_us-gaap_OtherLiabilitiesCurrent" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Other current liabilities</link:label>
    <link:label id="lab_us-gaap_OtherLiabilitiesCurrent_label_en-US" xlink:label="lab_us-gaap_OtherLiabilitiesCurrent" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Other Liabilities, Current</link:label>
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    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_OtherLiabilitiesCurrent" xlink:to="lab_us-gaap_OtherLiabilitiesCurrent" xlink:type="arc" order="1"/>
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    <link:label id="lab_codi_ProceedsHeldInEscrow_4c8bdaf6-7d12-4cfb-b191-b3c6daf2135a_terseLabel_en-US" xlink:label="lab_codi_ProceedsHeldInEscrow" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">proceeds held in escrow</link:label>
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    <link:label id="lab_us-gaap_AccountsReceivableGross_3bf3ea7e-bf17-465b-bb67-069504966351_terseLabel_en-US" xlink:label="lab_us-gaap_AccountsReceivableGross" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Accounts Receivable, before Allowance for Credit Loss</link:label>
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    <link:label id="lab_codi_MarucciBoaMember_8cd0c6db-3837-49a6-a22f-b5955a4dad15_terseLabel_en-US" xlink:label="lab_codi_MarucciBoaMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Marucci &amp; Boa</link:label>
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    <link:label id="lab_codi_A5.11TacticalMember_f07e7db6-4371-4c70-ab75-d994ac4641ea_terseLabel_en-US" xlink:label="lab_codi_A5.11TacticalMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">5.11</link:label>
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    <link:label id="lab_us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedAssets_e75dd2ca-1742-42ca-8db8-33c9acce75bf_totalLabel_en-US" xlink:label="lab_us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedAssets" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Business Combination, Recognized Identifiable Assets Acquired and Liabilities Assumed, Assets</link:label>
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    <link:label id="lab_codi_NonControllingInterestOfDiscontinuedOperationsMember_documentation_en-US" xlink:label="lab_codi_NonControllingInterestOfDiscontinuedOperationsMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Non-controlling interest of discontinued operations.</link:label>
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    <link:label id="lab_codi_PaymentsForRepurchaseSubsidiaryStock_663e6e40-62ea-424c-a86c-b8d9dbc97f43_terseLabel_en-US" xlink:label="lab_codi_PaymentsForRepurchaseSubsidiaryStock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Payments for Repurchase Subsidiary Stock</link:label>
    <link:label id="lab_codi_PaymentsForRepurchaseSubsidiaryStock_label_en-US" xlink:label="lab_codi_PaymentsForRepurchaseSubsidiaryStock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Payments for Repurchase Subsidiary Stock</link:label>
    <link:label id="lab_codi_PaymentsForRepurchaseSubsidiaryStock_documentation_en-US" xlink:label="lab_codi_PaymentsForRepurchaseSubsidiaryStock" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Payments for Repurchase Subsidiary Stock</link:label>
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    <link:label id="lab_us-gaap_SubsequentEventsTextBlock_502947dd-0e4e-4cd0-b0da-29b0f0ef1db4_terseLabel_en-US" xlink:label="lab_us-gaap_SubsequentEventsTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Subsequent Events</link:label>
    <link:label id="lab_us-gaap_SubsequentEventsTextBlock_label_en-US" xlink:label="lab_us-gaap_SubsequentEventsTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Subsequent Events [Text Block]</link:label>
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    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_SubsequentEventsTextBlock" xlink:to="lab_us-gaap_SubsequentEventsTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ScheduleOfEarningsPerShareBasicByCommonClassTextBlock_8337b888-7afb-4cb6-93c4-c50433c9eb5e_terseLabel_en-US" xlink:label="lab_us-gaap_ScheduleOfEarningsPerShareBasicByCommonClassTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Summary of Basic and Diluted Earnings Per Share</link:label>
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    <link:label id="lab_codi_SternoProductsMember_0f5abd50-b2a9-4ba6-8f08-23e250434040_terseLabel_en-US" xlink:label="lab_codi_SternoProductsMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Sterno</link:label>
    <link:label id="lab_codi_SternoProductsMember_label_en-US" xlink:label="lab_codi_SternoProductsMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Sterno Products [Member]</link:label>
    <link:label id="lab_codi_SternoProductsMember_documentation_en-US" xlink:label="lab_codi_SternoProductsMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Sterno Products [Member]</link:label>
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    <link:label id="lab_us-gaap_ComprehensiveIncomeNetOfTax_00061060-1126-41e9-a703-bdf182714c84_totalLabel_en-US" xlink:label="lab_us-gaap_ComprehensiveIncomeNetOfTax" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Comprehensive Income (Loss), Net of Tax, Attributable to Parent</link:label>
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    <link:label id="lab_us-gaap_IntangibleAssetsNetExcludingGoodwill_6d49e359-5558-48e4-877a-cc0c02dddd6f_terseLabel_en-US" xlink:label="lab_us-gaap_IntangibleAssetsNetExcludingGoodwill" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Intangible assets, net</link:label>
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    <link:label id="lab_us-gaap_NetCashProvidedByUsedInFinancingActivities_25152ad1-08fc-4d73-a39b-32d4d2c0d30f_totalLabel_en-US" xlink:label="lab_us-gaap_NetCashProvidedByUsedInFinancingActivities" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Net cash used in financing activities</link:label>
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    <link:label id="lab_us-gaap_OtherComprehensiveIncomeLossNetOfTaxPeriodIncreaseDecreaseAbstract_a46cde9c-c236-4276-af3a-95fee704806a_terseLabel_en-US" xlink:label="lab_us-gaap_OtherComprehensiveIncomeLossNetOfTaxPeriodIncreaseDecreaseAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Other comprehensive income</link:label>
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    <link:label id="lab_codi_PercentageOfGrossConsiderationReceived_3f2b2d38-c55b-4e4e-8f56-25b72282dc01_terseLabel_en-US" xlink:label="lab_codi_PercentageOfGrossConsiderationReceived" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Percentage of Gross Consideration Received</link:label>
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    <link:label id="lab_codi_PercentageOfGrossConsiderationReceived_documentation_en-US" xlink:label="lab_codi_PercentageOfGrossConsiderationReceived" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Percentage of Gross Consideration Received</link:label>
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    <link:label id="lab_codi_PercentageOwnershipFullyDilutedMember_918edb4e-fb44-4fc0-9422-b9781a07dc82_terseLabel_en-US" xlink:label="lab_codi_PercentageOwnershipFullyDilutedMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">% Ownership Fully Diluted</link:label>
    <link:label id="lab_codi_PercentageOwnershipFullyDilutedMember_label_en-US" xlink:label="lab_codi_PercentageOwnershipFullyDilutedMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Percentage Ownership Fully Diluted [Member]</link:label>
    <link:label id="lab_codi_PercentageOwnershipFullyDilutedMember_documentation_en-US" xlink:label="lab_codi_PercentageOwnershipFullyDilutedMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Percentage ownership fully diluted.</link:label>
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    <link:label id="lab_us-gaap_ScheduleOfEquityMethodInvestmentsLineItems_e7f47099-615a-47a6-b9f9-5bca9d0c82d5_terseLabel_en-US" xlink:label="lab_us-gaap_ScheduleOfEquityMethodInvestmentsLineItems" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Schedule of Equity Method Investments [Line Items]</link:label>
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    <link:label id="lab_srt_EuropeMember_d3c74ed1-9551-4b5a-a92a-ddc123b3091d_terseLabel_en-US" xlink:label="lab_srt_EuropeMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Europe</link:label>
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    <link:label id="lab_dei_EntityCurrentReportingStatus_51b59ecc-65f9-4041-a14f-ca44e2a12d81_terseLabel_en-US" xlink:label="lab_dei_EntityCurrentReportingStatus" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Entity Current Reporting Status</link:label>
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    <link:label id="lab_us-gaap_EarningsPerShareBasicAndDilutedAbstract_ed354306-a239-4954-8ee7-e98d17d976de_terseLabel_en-US" xlink:label="lab_us-gaap_EarningsPerShareBasicAndDilutedAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Basic income per common share attributable to Holdings (refer to Note J)</link:label>
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    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_EarningsPerShareBasicAndDilutedAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2021/elts/us-gaap-2021-01-31.xsd#us-gaap_EarningsPerShareBasicAndDilutedAbstract"/>
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    <link:label id="lab_us-gaap_DisposalGroupIncludingDiscontinuedOperationOtherNoncurrentLiabilities_e1682f1a-0875-4e8e-a36b-94618a1d4aab_terseLabel_en-US" xlink:label="lab_us-gaap_DisposalGroupIncludingDiscontinuedOperationOtherNoncurrentLiabilities" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Disposal Group, Including Discontinued Operation, Other Liabilities, Noncurrent</link:label>
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    <link:label id="lab_us-gaap_EffectiveIncomeTaxRateContinuingOperations_ac3dd3fa-8a0b-4e01-b138-d7a42fd3c172_totalLabel_en-US" xlink:label="lab_us-gaap_EffectiveIncomeTaxRateContinuingOperations" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Effective income tax rate</link:label>
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    <link:label id="lab_codi_PropertyPlantAndEquipmentAndInventoryTextBlock_6d139df0-d27b-4d7b-a60a-3c1115ee0672_terseLabel_en-US" xlink:label="lab_codi_PropertyPlantAndEquipmentAndInventoryTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Property, Plant and Equipment and Inventory</link:label>
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    <link:label id="lab_us-gaap_SeriesAPreferredStockMember_8a1752b6-0d72-4302-8a7f-d9d8c0a8717b_terseLabel_en-US" xlink:label="lab_us-gaap_SeriesAPreferredStockMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Series A Preferred Stock</link:label>
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    <link:label id="lab_us-gaap_ProfitLoss_554714a6-c367-4fb2-8e29-3dfeb88004ba_terseLabel_en-US" xlink:label="lab_us-gaap_ProfitLoss" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Net income</link:label>
    <link:label id="lab_us-gaap_ProfitLoss_label_en-US" xlink:label="lab_us-gaap_ProfitLoss" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Net Income (Loss), Including Portion Attributable to Noncontrolling Interest</link:label>
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    <link:label id="lab_us-gaap_AmortizationOfFinancingCosts_56510a0d-71c6-4898-aa02-b1c1a6cb21e3_negatedLabel_en-US" xlink:label="lab_us-gaap_AmortizationOfFinancingCosts" xlink:role="http://www.xbrl.org/2009/role/negatedLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Amortization of debt issuance costs</link:label>
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    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AmortizationOfFinancingCosts" xlink:href="https://xbrl.fasb.org/us-gaap/2021/elts/us-gaap-2021-01-31.xsd#us-gaap_AmortizationOfFinancingCosts"/>
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    <link:label id="lab_us-gaap_InventoryValuationReserves_5fb703dd-e01e-4dbc-b177-a1a000a7ebb3_negatedLabel_en-US" xlink:label="lab_us-gaap_InventoryValuationReserves" xlink:role="http://www.xbrl.org/2009/role/negatedLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Less: obsolescence reserve</link:label>
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    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_InventoryValuationReserves" xlink:to="lab_us-gaap_InventoryValuationReserves" xlink:type="arc" order="1"/>
    <link:label id="lab_codi_A2018CreditFacilityMember_31d18a7f-49d1-465b-bcdf-6a9aade48d12_terseLabel_en-US" xlink:label="lab_codi_A2018CreditFacilityMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">2018 Credit Facility</link:label>
    <link:label id="lab_codi_A2018CreditFacilityMember_label_en-US" xlink:label="lab_codi_A2018CreditFacilityMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">2018 Credit Facility [Member]</link:label>
    <link:label id="lab_codi_A2018CreditFacilityMember_documentation_en-US" xlink:label="lab_codi_A2018CreditFacilityMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">2018 Credit Facility</link:label>
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    <link:label id="lab_us-gaap_SharesIssued_95489886-b957-4fee-b55b-82dc605640dc_terseLabel_en-US" xlink:label="lab_us-gaap_SharesIssued" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Shares, Issued</link:label>
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    <link:label id="lab_us-gaap_OtherOwnershipInterestsNameDomain_eb744697-4539-4709-9124-8dd6aa456feb_terseLabel_en-US" xlink:label="lab_us-gaap_OtherOwnershipInterestsNameDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Other Ownership Interests, Name [Domain]</link:label>
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    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OtherOwnershipInterestsNameDomain" xlink:href="https://xbrl.fasb.org/us-gaap/2021/elts/us-gaap-2021-01-31.xsd#us-gaap_OtherOwnershipInterestsNameDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_OtherOwnershipInterestsNameDomain" xlink:to="lab_us-gaap_OtherOwnershipInterestsNameDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_country_US_70f0f3bc-5194-4985-a94d-f4859424420b_terseLabel_en-US" xlink:label="lab_country_US" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">United States</link:label>
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    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_StatementOfIncomeAndComprehensiveIncomeAbstract" xlink:to="lab_us-gaap_StatementOfIncomeAndComprehensiveIncomeAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AssetsCurrentAbstract_167cf6b0-a6da-4934-93da-02902d6941f3_terseLabel_en-US" xlink:label="lab_us-gaap_AssetsCurrentAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Current assets:</link:label>
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    <link:label id="lab_us-gaap_InterestIncomeExpenseNonoperatingNet_53044219-57f7-4354-a531-c07fe9491743_terseLabel_en-US" xlink:label="lab_us-gaap_InterestIncomeExpenseNonoperatingNet" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Interest expense, net</link:label>
    <link:label id="lab_us-gaap_InterestIncomeExpenseNonoperatingNet_label_en-US" xlink:label="lab_us-gaap_InterestIncomeExpenseNonoperatingNet" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Interest Income (Expense), Nonoperating, Net</link:label>
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    <link:label id="lab_us-gaap_LeasesAbstract_ed98b467-a163-4e4e-ac05-ee249c96b887_terseLabel_en-US" xlink:label="lab_us-gaap_LeasesAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Leases [Abstract]</link:label>
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    <link:label id="lab_us-gaap_DisposalGroupIncludingDiscontinuedOperationCashAndCashEquivalents_0690e557-5bf4-4cab-bb71-9b6ce694196d_terseLabel_en-US" xlink:label="lab_us-gaap_DisposalGroupIncludingDiscontinuedOperationCashAndCashEquivalents" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Disposal Group, Including Discontinued Operation, Cash and Cash Equivalents</link:label>
    <link:label id="lab_us-gaap_DisposalGroupIncludingDiscontinuedOperationCashAndCashEquivalents_label_en-US" xlink:label="lab_us-gaap_DisposalGroupIncludingDiscontinuedOperationCashAndCashEquivalents" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Disposal Group, Including Discontinued Operation, Cash and Cash Equivalents</link:label>
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    <link:label id="lab_us-gaap_LondonInterbankOfferedRateLIBORMember_6a9e5ad2-42fc-4cd7-9829-db4a220350ed_terseLabel_en-US" xlink:label="lab_us-gaap_LondonInterbankOfferedRateLIBORMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">London Interbank Offered Rate (LIBOR)</link:label>
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    <link:label id="lab_us-gaap_IncomeLossFromDiscontinuedOperationsNetOfTaxAttributableToReportingEntity_fc7c92f5-a2ba-4a5c-b738-a4f6e304e08a_terseLabel_en-US" xlink:label="lab_us-gaap_IncomeLossFromDiscontinuedOperationsNetOfTaxAttributableToReportingEntity" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Income from discontinued operations, net of income tax</link:label>
    <link:label id="lab_us-gaap_IncomeLossFromDiscontinuedOperationsNetOfTaxAttributableToReportingEntity_label_en-US" xlink:label="lab_us-gaap_IncomeLossFromDiscontinuedOperationsNetOfTaxAttributableToReportingEntity" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Income (Loss) from Discontinued Operations, Net of Tax, Attributable to Parent</link:label>
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    <link:label id="lab_us-gaap_DisposalGroupClassificationDomain_50632a31-3cf3-4bfd-b16a-ee4bdf9ff576_terseLabel_en-US" xlink:label="lab_us-gaap_DisposalGroupClassificationDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Disposal Group Classification [Domain]</link:label>
    <link:label id="lab_us-gaap_DisposalGroupClassificationDomain_label_en-US" xlink:label="lab_us-gaap_DisposalGroupClassificationDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Disposal Group Classification [Domain]</link:label>
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    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DisposalGroupClassificationDomain" xlink:to="lab_us-gaap_DisposalGroupClassificationDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_EntityAddressPostalZipCode_28528c2e-b495-42d5-b785-c56024b11c3d_terseLabel_en-US" xlink:label="lab_dei_EntityAddressPostalZipCode" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Entity Address, Postal Zip Code</link:label>
    <link:label id="lab_dei_EntityAddressPostalZipCode_label_en-US" xlink:label="lab_dei_EntityAddressPostalZipCode" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Entity Address, Postal Zip Code</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_EntityAddressPostalZipCode" xlink:href="https://xbrl.sec.gov/dei/2021q4/dei-2021q4.xsd#dei_EntityAddressPostalZipCode"/>
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    <link:label id="lab_us-gaap_WeightedAverageNumberOfDilutedSharesOutstanding_2ddbcef3-0b8d-43c2-8e1a-7904218c6757_terseLabel_en-US" xlink:label="lab_us-gaap_WeightedAverageNumberOfDilutedSharesOutstanding" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Weighted Average Number of Shares Outstanding, Diluted</link:label>
    <link:label id="lab_us-gaap_WeightedAverageNumberOfDilutedSharesOutstanding_label_en-US" xlink:label="lab_us-gaap_WeightedAverageNumberOfDilutedSharesOutstanding" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Weighted Average Number of Shares Outstanding, Diluted</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_WeightedAverageNumberOfDilutedSharesOutstanding" xlink:href="https://xbrl.fasb.org/us-gaap/2021/elts/us-gaap-2021-01-31.xsd#us-gaap_WeightedAverageNumberOfDilutedSharesOutstanding"/>
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    <link:label id="lab_us-gaap_FairValueMeasurementsRecurringMember_b88fe2f3-cbd6-4121-a01c-2dda25ae06bd_terseLabel_en-US" xlink:label="lab_us-gaap_FairValueMeasurementsRecurringMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Fair Value, Measurements, Recurring</link:label>
    <link:label id="lab_us-gaap_FairValueMeasurementsRecurringMember_label_en-US" xlink:label="lab_us-gaap_FairValueMeasurementsRecurringMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Fair Value, Recurring [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FairValueMeasurementsRecurringMember" xlink:href="https://xbrl.fasb.org/us-gaap/2021/elts/us-gaap-2021-01-31.xsd#us-gaap_FairValueMeasurementsRecurringMember"/>
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    <link:label id="lab_us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedLiabilitiesAbstract_bef373ee-f5aa-4252-8835-1ea4d609594e_terseLabel_en-US" xlink:label="lab_us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedLiabilitiesAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Liabilities and noncontrolling interest:</link:label>
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    <link:label id="lab_us-gaap_IncomeTaxDisclosureTextBlock_33f75f4e-1a81-496d-8a42-1fd5aa4b3363_terseLabel_en-US" xlink:label="lab_us-gaap_IncomeTaxDisclosureTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Income Taxes</link:label>
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    <link:label id="lab_us-gaap_LiabilitiesOfDisposalGroupIncludingDiscontinuedOperationNoncurrent_8db4dc48-1ff1-4328-b9a5-b2064a79af4e_terseLabel_en-US" xlink:label="lab_us-gaap_LiabilitiesOfDisposalGroupIncludingDiscontinuedOperationNoncurrent" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Disposal Group, Including Discontinued Operation, Liabilities, Noncurrent</link:label>
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    <link:label id="lab_us-gaap_TradingRevenueMember_dfd3073b-c3dd-48f6-9aee-f883f7f05c11_terseLabel_en-US" xlink:label="lab_us-gaap_TradingRevenueMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Trading Revenue</link:label>
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    <link:label id="lab_us-gaap_PortionAtFairValueFairValueDisclosureMember_0f7c7aac-dbcc-4dce-a17b-68cece6a05ee_terseLabel_en-US" xlink:label="lab_us-gaap_PortionAtFairValueFairValueDisclosureMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Portion at Fair Value Measurement [Member]</link:label>
    <link:label id="lab_us-gaap_PortionAtFairValueFairValueDisclosureMember_label_en-US" xlink:label="lab_us-gaap_PortionAtFairValueFairValueDisclosureMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Portion at Fair Value Measurement [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PortionAtFairValueFairValueDisclosureMember" xlink:href="https://xbrl.fasb.org/us-gaap/2021/elts/us-gaap-2021-01-31.xsd#us-gaap_PortionAtFairValueFairValueDisclosureMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_PortionAtFairValueFairValueDisclosureMember" xlink:to="lab_us-gaap_PortionAtFairValueFairValueDisclosureMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ReconciliationOfOperatingProfitLossFromSegmentsToConsolidatedTextBlock_51d200a7-7647-44fe-b9e9-4dcaba17c186_terseLabel_en-US" xlink:label="lab_us-gaap_ReconciliationOfOperatingProfitLossFromSegmentsToConsolidatedTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Summary of Profit (Loss) of Operating Segments</link:label>
    <link:label id="lab_us-gaap_ReconciliationOfOperatingProfitLossFromSegmentsToConsolidatedTextBlock_label_en-US" xlink:label="lab_us-gaap_ReconciliationOfOperatingProfitLossFromSegmentsToConsolidatedTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Reconciliation of Operating Profit (Loss) from Segments to Consolidated [Table Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ReconciliationOfOperatingProfitLossFromSegmentsToConsolidatedTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2021/elts/us-gaap-2021-01-31.xsd#us-gaap_ReconciliationOfOperatingProfitLossFromSegmentsToConsolidatedTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ReconciliationOfOperatingProfitLossFromSegmentsToConsolidatedTextBlock" xlink:to="lab_us-gaap_ReconciliationOfOperatingProfitLossFromSegmentsToConsolidatedTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_IncreaseDecreaseInOperatingCapitalAbstract_68213d5f-02e0-4571-9a18-a6ddbbd4da2b_terseLabel_en-US" xlink:label="lab_us-gaap_IncreaseDecreaseInOperatingCapitalAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Changes in operating assets and liabilities, net of acquisitions:</link:label>
    <link:label id="lab_us-gaap_IncreaseDecreaseInOperatingCapitalAbstract_label_en-US" xlink:label="lab_us-gaap_IncreaseDecreaseInOperatingCapitalAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Increase (Decrease) in Operating Capital [Abstract]</link:label>
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    <link:label id="lab_us-gaap_AccumulatedDepreciationDepletionAndAmortizationPropertyPlantAndEquipment_c7a593c3-f931-4b64-997a-3d2ec10ec1e5_negatedLabel_en-US" xlink:label="lab_us-gaap_AccumulatedDepreciationDepletionAndAmortizationPropertyPlantAndEquipment" xlink:role="http://www.xbrl.org/2009/role/negatedLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Less: accumulated depreciation</link:label>
    <link:label id="lab_us-gaap_AccumulatedDepreciationDepletionAndAmortizationPropertyPlantAndEquipment_label_en-US" xlink:label="lab_us-gaap_AccumulatedDepreciationDepletionAndAmortizationPropertyPlantAndEquipment" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Accumulated Depreciation, Depletion and Amortization, Property, Plant, and Equipment</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AccumulatedDepreciationDepletionAndAmortizationPropertyPlantAndEquipment" xlink:href="https://xbrl.fasb.org/us-gaap/2021/elts/us-gaap-2021-01-31.xsd#us-gaap_AccumulatedDepreciationDepletionAndAmortizationPropertyPlantAndEquipment"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AccumulatedDepreciationDepletionAndAmortizationPropertyPlantAndEquipment" xlink:to="lab_us-gaap_AccumulatedDepreciationDepletionAndAmortizationPropertyPlantAndEquipment" xlink:type="arc" order="1"/>
    <link:label id="lab_codi_CleanEarthHoldingsMember_1b9b58ed-2411-4795-9320-289339acf4d6_terseLabel_en-US" xlink:label="lab_codi_CleanEarthHoldingsMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Clean Earth</link:label>
    <link:label id="lab_codi_CleanEarthHoldingsMember_label_en-US" xlink:label="lab_codi_CleanEarthHoldingsMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Clean Earth Holdings [Member]</link:label>
    <link:label id="lab_codi_CleanEarthHoldingsMember_documentation_en-US" xlink:label="lab_codi_CleanEarthHoldingsMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Clean Earth Holdings [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_codi_CleanEarthHoldingsMember" xlink:href="codi-20220331.xsd#codi_CleanEarthHoldingsMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_codi_CleanEarthHoldingsMember" xlink:to="lab_codi_CleanEarthHoldingsMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_NetCashProvidedByUsedInOperatingActivitiesAbstract_3be60d1e-e5b1-4add-b5b0-0cf3db1d1ba2_terseLabel_en-US" xlink:label="lab_us-gaap_NetCashProvidedByUsedInOperatingActivitiesAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Cash flows from operating activities:</link:label>
    <link:label id="lab_us-gaap_NetCashProvidedByUsedInOperatingActivitiesAbstract_label_en-US" xlink:label="lab_us-gaap_NetCashProvidedByUsedInOperatingActivitiesAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Net Cash Provided by (Used in) Operating Activities [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_NetCashProvidedByUsedInOperatingActivitiesAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2021/elts/us-gaap-2021-01-31.xsd#us-gaap_NetCashProvidedByUsedInOperatingActivitiesAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_NetCashProvidedByUsedInOperatingActivitiesAbstract" xlink:to="lab_us-gaap_NetCashProvidedByUsedInOperatingActivitiesAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_SeriesBMember_e758f6a5-ce0a-40a3-b68c-371e9431ff9c_terseLabel_en-US" xlink:label="lab_us-gaap_SeriesBMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Series B [Member]</link:label>
    <link:label id="lab_us-gaap_SeriesBMember_label_en-US" xlink:label="lab_us-gaap_SeriesBMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Series B [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_SeriesBMember" xlink:href="https://xbrl.fasb.org/us-gaap/2021/elts/us-gaap-2021-01-31.xsd#us-gaap_SeriesBMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_SeriesBMember" xlink:to="lab_us-gaap_SeriesBMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ConsolidationPolicyTextBlock_e9258b30-07a9-4171-9bdf-8025538a471a_terseLabel_en-US" xlink:label="lab_us-gaap_ConsolidationPolicyTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Consolidation</link:label>
    <link:label id="lab_us-gaap_ConsolidationPolicyTextBlock_label_en-US" xlink:label="lab_us-gaap_ConsolidationPolicyTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Consolidation, Policy [Policy Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ConsolidationPolicyTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2021/elts/us-gaap-2021-01-31.xsd#us-gaap_ConsolidationPolicyTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ConsolidationPolicyTextBlock" xlink:to="lab_us-gaap_ConsolidationPolicyTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_EntityShellCompany_0507dc1f-d0e5-4a51-b563-afec7c9e397c_terseLabel_en-US" xlink:label="lab_dei_EntityShellCompany" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Entity Shell Company</link:label>
    <link:label id="lab_dei_EntityShellCompany_label_en-US" xlink:label="lab_dei_EntityShellCompany" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Entity Shell Company</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_EntityShellCompany" xlink:href="https://xbrl.sec.gov/dei/2021q4/dei-2021q4.xsd#dei_EntityShellCompany"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_EntityShellCompany" xlink:to="lab_dei_EntityShellCompany" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LiabilitiesCurrent_4af9343a-2977-4833-b13c-8e780606f92a_totalLabel_en-US" xlink:label="lab_us-gaap_LiabilitiesCurrent" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Total current liabilities</link:label>
    <link:label id="lab_us-gaap_LiabilitiesCurrent_label_en-US" xlink:label="lab_us-gaap_LiabilitiesCurrent" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Liabilities, Current</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LiabilitiesCurrent" xlink:href="https://xbrl.fasb.org/us-gaap/2021/elts/us-gaap-2021-01-31.xsd#us-gaap_LiabilitiesCurrent"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LiabilitiesCurrent" xlink:to="lab_us-gaap_LiabilitiesCurrent" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ClassOfStockDomain_d2a1bf15-cfe6-4c5f-b4fb-45ac5b4ad79b_terseLabel_en-US" xlink:label="lab_us-gaap_ClassOfStockDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Class of Stock [Domain]</link:label>
    <link:label id="lab_us-gaap_ClassOfStockDomain_label_en-US" xlink:label="lab_us-gaap_ClassOfStockDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Class of Stock [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ClassOfStockDomain" xlink:href="https://xbrl.fasb.org/us-gaap/2021/elts/us-gaap-2021-01-31.xsd#us-gaap_ClassOfStockDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ClassOfStockDomain" xlink:to="lab_us-gaap_ClassOfStockDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_PaymentsToAcquireBusinessesGross_a463409f-9a03-48ef-ad39-3621d56a6133_terseLabel_en-US" xlink:label="lab_us-gaap_PaymentsToAcquireBusinessesGross" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Payments to Acquire Businesses, Gross</link:label>
    <link:label id="lab_us-gaap_PaymentsToAcquireBusinessesGross_label_en-US" xlink:label="lab_us-gaap_PaymentsToAcquireBusinessesGross" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Payments to Acquire Businesses, Gross</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PaymentsToAcquireBusinessesGross" xlink:href="https://xbrl.fasb.org/us-gaap/2021/elts/us-gaap-2021-01-31.xsd#us-gaap_PaymentsToAcquireBusinessesGross"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_PaymentsToAcquireBusinessesGross" xlink:to="lab_us-gaap_PaymentsToAcquireBusinessesGross" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LineOfCreditFacilityMaximumBorrowingCapacity_8930ad73-6763-43d3-bd1e-1775f3d0fcf9_terseLabel_en-US" xlink:label="lab_us-gaap_LineOfCreditFacilityMaximumBorrowingCapacity" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Line of Credit Facility, Maximum Borrowing Capacity</link:label>
    <link:label id="lab_us-gaap_LineOfCreditFacilityMaximumBorrowingCapacity_label_en-US" xlink:label="lab_us-gaap_LineOfCreditFacilityMaximumBorrowingCapacity" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Line of Credit Facility, Maximum Borrowing Capacity</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LineOfCreditFacilityMaximumBorrowingCapacity" xlink:href="https://xbrl.fasb.org/us-gaap/2021/elts/us-gaap-2021-01-31.xsd#us-gaap_LineOfCreditFacilityMaximumBorrowingCapacity"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LineOfCreditFacilityMaximumBorrowingCapacity" xlink:to="lab_us-gaap_LineOfCreditFacilityMaximumBorrowingCapacity" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedCashAndEquivalents_99f6f581-539c-4060-80dd-eed37f272da9_terseLabel_en-US" xlink:label="lab_us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedCashAndEquivalents" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Business Combination, Recognized Identifiable Assets Acquired and Liabilities Assumed, Cash and Equivalents</link:label>
    <link:label id="lab_us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedCashAndEquivalents_label_en-US" xlink:label="lab_us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedCashAndEquivalents" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Business Combination, Recognized Identifiable Assets Acquired and Liabilities Assumed, Cash and Equivalents</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedCashAndEquivalents" xlink:href="https://xbrl.fasb.org/us-gaap/2021/elts/us-gaap-2021-01-31.xsd#us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedCashAndEquivalents"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedCashAndEquivalents" xlink:to="lab_us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedCashAndEquivalents" xlink:type="arc" order="1"/>
    <link:label id="lab_srt_OwnershipDomain_a7727dbb-406b-4212-a25b-c4b4c1c88e8a_terseLabel_en-US" xlink:label="lab_srt_OwnershipDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Ownership [Domain]</link:label>
    <link:label id="lab_srt_OwnershipDomain_label_en-US" xlink:label="lab_srt_OwnershipDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Ownership [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_srt_OwnershipDomain" xlink:href="https://xbrl.fasb.org/srt/2021/elts/srt-2021-01-31.xsd#srt_OwnershipDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_srt_OwnershipDomain" xlink:to="lab_srt_OwnershipDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_SegmentReportingInformationLineItems_65d3a8d4-2877-43a0-800d-165f2198046c_terseLabel_en-US" xlink:label="lab_us-gaap_SegmentReportingInformationLineItems" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Segment Reporting Information [Line Items]</link:label>
    <link:label id="lab_us-gaap_SegmentReportingInformationLineItems_label_en-US" xlink:label="lab_us-gaap_SegmentReportingInformationLineItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Segment Reporting Information [Line Items]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_SegmentReportingInformationLineItems" xlink:href="https://xbrl.fasb.org/us-gaap/2021/elts/us-gaap-2021-01-31.xsd#us-gaap_SegmentReportingInformationLineItems"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_SegmentReportingInformationLineItems" xlink:to="lab_us-gaap_SegmentReportingInformationLineItems" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_CurrentFiscalYearEndDate_5ab5c901-366e-4677-bc8c-095d70f3bfc1_terseLabel_en-US" xlink:label="lab_dei_CurrentFiscalYearEndDate" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Current Fiscal Year End Date</link:label>
    <link:label id="lab_dei_CurrentFiscalYearEndDate_label_en-US" xlink:label="lab_dei_CurrentFiscalYearEndDate" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Current Fiscal Year End Date</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_CurrentFiscalYearEndDate" xlink:href="https://xbrl.sec.gov/dei/2021q4/dei-2021q4.xsd#dei_CurrentFiscalYearEndDate"/>
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    <link:label id="lab_us-gaap_FiniteLivedIntangibleAssetsNet_22d1fb41-3543-4fa2-9a07-47e00c1109b6_terseLabel_en-US" xlink:label="lab_us-gaap_FiniteLivedIntangibleAssetsNet" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Finite-Lived Intangible Assets, Net</link:label>
    <link:label id="lab_us-gaap_FiniteLivedIntangibleAssetsNet_label_en-US" xlink:label="lab_us-gaap_FiniteLivedIntangibleAssetsNet" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Finite-Lived Intangible Assets, Net</link:label>
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    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FiniteLivedIntangibleAssetsNet" xlink:to="lab_us-gaap_FiniteLivedIntangibleAssetsNet" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_Goodwill_d1eb2a1c-9c59-457a-a909-44b475b555d5_terseLabel_en-US" xlink:label="lab_us-gaap_Goodwill" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Goodwill</link:label>
    <link:label id="lab_us-gaap_Goodwill_b65aa0fb-9c27-4639-8168-963785de38de_totalLabel_en-US" xlink:label="lab_us-gaap_Goodwill" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Goodwill - net carrying amount</link:label>
    <link:label id="lab_us-gaap_Goodwill_12abb774-2ca8-48b4-a20f-236e82930a83_periodEndLabel_en-US" xlink:label="lab_us-gaap_Goodwill" xlink:role="http://www.xbrl.org/2003/role/periodEndLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Balance as of January 1, 2017</link:label>
    <link:label id="lab_us-gaap_Goodwill_a72afdf3-9ff5-468d-9257-89b28afc4e3f_periodStartLabel_en-US" xlink:label="lab_us-gaap_Goodwill" xlink:role="http://www.xbrl.org/2003/role/periodStartLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Balance as of March 31, 2017</link:label>
    <link:label id="lab_us-gaap_Goodwill_label_en-US" xlink:label="lab_us-gaap_Goodwill" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Goodwill</link:label>
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    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_Goodwill" xlink:to="lab_us-gaap_Goodwill" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_OperatingLeaseRightOfUseAssetStatementOfFinancialPositionExtensibleList_f0bf7796-ba9e-47c7-a29b-8253a61303de_terseLabel_en-US" xlink:label="lab_us-gaap_OperatingLeaseRightOfUseAssetStatementOfFinancialPositionExtensibleList" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Operating Lease, Right-of-Use Asset, Statement of Financial Position [Extensible Enumeration]</link:label>
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    <link:label id="lab_us-gaap_MinorityInterest_a59d1415-968d-470e-9e36-0a3300d33795_terseLabel_en-US" xlink:label="lab_us-gaap_MinorityInterest" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Noncontrolling interest</link:label>
    <link:label id="lab_us-gaap_MinorityInterest_41f3e356-9985-471e-ada4-58a762b58378_verboseLabel_en-US" xlink:label="lab_us-gaap_MinorityInterest" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Noncontrolling interest of discontinued operations</link:label>
    <link:label id="lab_us-gaap_MinorityInterest_label_en-US" xlink:label="lab_us-gaap_MinorityInterest" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Stockholders' Equity Attributable to Noncontrolling Interest</link:label>
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    <link:label id="lab_codi_MarucciMemberMember_b6428cd2-76c8-41ee-8a9a-384c58f4e605_terseLabel_en-US" xlink:label="lab_codi_MarucciMemberMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Marucci [Member]</link:label>
    <link:label id="lab_codi_MarucciMemberMember_label_en-US" xlink:label="lab_codi_MarucciMemberMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Marucci [Member] [Member]</link:label>
    <link:label id="lab_codi_MarucciMemberMember_documentation_en-US" xlink:label="lab_codi_MarucciMemberMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Marucci [Member] [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_codi_MarucciMemberMember" xlink:href="codi-20220331.xsd#codi_MarucciMemberMember"/>
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    <link:label id="lab_us-gaap_ConstructionInProgressGross_f9f95497-3654-40f3-b8c8-9c5623f583d4_terseLabel_en-US" xlink:label="lab_us-gaap_ConstructionInProgressGross" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Construction in process</link:label>
    <link:label id="lab_us-gaap_ConstructionInProgressGross_label_en-US" xlink:label="lab_us-gaap_ConstructionInProgressGross" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Construction in Progress, Gross</link:label>
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    <link:label id="lab_us-gaap_IncomeLossFromContinuingOperationsIncludingPortionAttributableToNoncontrollingInterest_70741b64-5bd6-46d7-8379-94aba0d7e405_terseLabel_en-US" xlink:label="lab_us-gaap_IncomeLossFromContinuingOperationsIncludingPortionAttributableToNoncontrollingInterest" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Income from continuing operations</link:label>
    <link:label id="lab_us-gaap_IncomeLossFromContinuingOperationsIncludingPortionAttributableToNoncontrollingInterest_label_en-US" xlink:label="lab_us-gaap_IncomeLossFromContinuingOperationsIncludingPortionAttributableToNoncontrollingInterest" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Income (Loss) from Continuing Operations, Net of Tax, Including Portion Attributable to Noncontrolling Interest</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_IncomeLossFromContinuingOperationsIncludingPortionAttributableToNoncontrollingInterest" xlink:href="https://xbrl.fasb.org/us-gaap/2021/elts/us-gaap-2021-01-31.xsd#us-gaap_IncomeLossFromContinuingOperationsIncludingPortionAttributableToNoncontrollingInterest"/>
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    <link:label id="lab_codi_DistributorRelationsAndOtherMember_7de67db5-8378-4b7d-94e4-a0935d8d0c83_terseLabel_en-US" xlink:label="lab_codi_DistributorRelationsAndOtherMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Other contractual intangible assets</link:label>
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    <link:label id="lab_codi_DistributorRelationsAndOtherMember_documentation_en-US" xlink:label="lab_codi_DistributorRelationsAndOtherMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Distributor relations and other.</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_codi_DistributorRelationsAndOtherMember" xlink:href="codi-20220331.xsd#codi_DistributorRelationsAndOtherMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_codi_DistributorRelationsAndOtherMember" xlink:to="lab_codi_DistributorRelationsAndOtherMember" xlink:type="arc" order="1"/>
    <link:label id="lab_codi_LuganoMember_ca172a91-0120-493f-b614-f88f11345e04_terseLabel_en-US" xlink:label="lab_codi_LuganoMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Lugano</link:label>
    <link:label id="lab_codi_LuganoMember_label_en-US" xlink:label="lab_codi_LuganoMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Lugano [Member]</link:label>
    <link:label id="lab_codi_LuganoMember_documentation_en-US" xlink:label="lab_codi_LuganoMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Lugano</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_codi_LuganoMember" xlink:href="codi-20220331.xsd#codi_LuganoMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_codi_LuganoMember" xlink:to="lab_codi_LuganoMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ScheduleOfGoodwillTextBlock_d374a86d-fafb-4b45-8603-627c70f52dc1_terseLabel_en-US" xlink:label="lab_us-gaap_ScheduleOfGoodwillTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Summary of Reconciliation of Change in Carrying Value of Goodwill</link:label>
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    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ScheduleOfGoodwillTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2021/elts/us-gaap-2021-01-31.xsd#us-gaap_ScheduleOfGoodwillTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ScheduleOfGoodwillTextBlock" xlink:to="lab_us-gaap_ScheduleOfGoodwillTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_codi_DisposalGroupIncludingDiscontinuedOperationIntercompanyInterestExpenseExcludedfromIncomeLossfromDiscontinuedOperations_f96abb34-054f-458c-aae2-6e66bad47dfc_terseLabel_en-US" xlink:label="lab_codi_DisposalGroupIncludingDiscontinuedOperationIntercompanyInterestExpenseExcludedfromIncomeLossfromDiscontinuedOperations" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Disposal Group, Including Discontinued Operation, Intercompany Interest Expense Excluded from Income (Loss) from Discontinued Operations</link:label>
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    <link:loc xlink:type="locator" xlink:label="loc_codi_DisposalGroupIncludingDiscontinuedOperationIntercompanyInterestExpenseExcludedfromIncomeLossfromDiscontinuedOperations" xlink:href="codi-20220331.xsd#codi_DisposalGroupIncludingDiscontinuedOperationIntercompanyInterestExpenseExcludedfromIncomeLossfromDiscontinuedOperations"/>
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    <link:label id="lab_codi_PaymentstoAcquireBusinessesNetofCashAcquiredandNetofTransactionsCosts_9c6e0aa9-4202-4964-b077-d3f55d0a4887_terseLabel_en-US" xlink:label="lab_codi_PaymentstoAcquireBusinessesNetofCashAcquiredandNetofTransactionsCosts" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Payments to Acquire Businesses, Net of Cash Acquired and Net of Transactions Costs</link:label>
    <link:label id="lab_codi_PaymentstoAcquireBusinessesNetofCashAcquiredandNetofTransactionsCosts_label_en-US" xlink:label="lab_codi_PaymentstoAcquireBusinessesNetofCashAcquiredandNetofTransactionsCosts" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Payments to Acquire Businesses, Net of Cash Acquired and Net of Transactions Costs</link:label>
    <link:label id="lab_codi_PaymentstoAcquireBusinessesNetofCashAcquiredandNetofTransactionsCosts_documentation_en-US" xlink:label="lab_codi_PaymentstoAcquireBusinessesNetofCashAcquiredandNetofTransactionsCosts" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Payments to Acquire Businesses, Net of Cash Acquired and Net of Transactions Costs</link:label>
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