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    <link:label id="lab_us-gaap_LiabilitiesCurrent_61611fe6-5645-4bed-8ab0-736c9abf1f09_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>
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    <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"/>
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    <link:label id="lab_codi_DistributionsPayableAmountPerShare_documentation_en-US" xlink:label="lab_codi_DistributionsPayableAmountPerShare" 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">Distributions payable amount per share.</link:label>
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    <link:label id="lab_us-gaap_GeographicDistributionForeignMember_415cff47-1cdd-4cf7-9a59-8b2fb3b2ab23_terseLabel_en-US" xlink:label="lab_us-gaap_GeographicDistributionForeignMember" 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">Outside of the United States</link:label>
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    <link:label id="lab_codi_NumberOfManufacturingFacilities_08286e8a-aedb-4dc4-ac64-ad929837172b_terseLabel_en-US" xlink:label="lab_codi_NumberOfManufacturingFacilities" 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">Number Of Manufacturing Facilities</link:label>
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    <link:label id="lab_codi_NumberOfManufacturingFacilities_documentation_en-US" xlink:label="lab_codi_NumberOfManufacturingFacilities" 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">Number of manufacturing facilities.</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_codi_NumberOfManufacturingFacilities" xlink:href="codi-20200930.xsd#codi_NumberOfManufacturingFacilities"/>
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    <link:label id="lab_us-gaap_ScheduleOfBusinessAcquisitionsByAcquisitionTable_229dcefe-ec23-4258-b5bb-aa8fff0cba79_terseLabel_en-US" xlink:label="lab_us-gaap_ScheduleOfBusinessAcquisitionsByAcquisitionTable" 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 Business Acquisitions, by Acquisition [Table]</link:label>
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    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ScheduleOfBusinessAcquisitionsByAcquisitionTable" xlink:href="http://xbrl.fasb.org/us-gaap/2020/elts/us-gaap-2020-01-31.xsd#us-gaap_ScheduleOfBusinessAcquisitionsByAcquisitionTable"/>
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    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_NoncontrollingInterestIncreaseFromBusinessCombination" xlink:href="http://xbrl.fasb.org/us-gaap/2020/elts/us-gaap-2020-01-31.xsd#us-gaap_NoncontrollingInterestIncreaseFromBusinessCombination"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_NoncontrollingInterestIncreaseFromBusinessCombination" xlink:to="lab_us-gaap_NoncontrollingInterestIncreaseFromBusinessCombination" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AssetsAbstract_4f2eae81-d50d-49ca-ad8b-ad91e865e671_terseLabel_en-US" xlink:label="lab_us-gaap_AssetsAbstract" 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">Assets</link:label>
    <link:label id="lab_us-gaap_AssetsAbstract_label_en-US" xlink:label="lab_us-gaap_AssetsAbstract" 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">Assets [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AssetsAbstract" xlink:href="http://xbrl.fasb.org/us-gaap/2020/elts/us-gaap-2020-01-31.xsd#us-gaap_AssetsAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AssetsAbstract" xlink:to="lab_us-gaap_AssetsAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_srt_ScheduleOfEquityMethodInvestmentEquityMethodInvesteeNameAxis_4ca71c01-09bb-4761-be0c-9bae8d3852eb_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>
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    <link:loc xlink:type="locator" xlink:label="loc_srt_ScheduleOfEquityMethodInvestmentEquityMethodInvesteeNameAxis" xlink:href="http://xbrl.fasb.org/srt/2020/elts/srt-2020-01-31.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_us-gaap_ScheduleOfPropertyPlantAndEquipmentTable_883b9f62-c8b5-4839-ad04-0fadd1749716_terseLabel_en-US" xlink:label="lab_us-gaap_ScheduleOfPropertyPlantAndEquipmentTable" 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 [Table]</link:label>
    <link:label id="lab_us-gaap_ScheduleOfPropertyPlantAndEquipmentTable_label_en-US" xlink:label="lab_us-gaap_ScheduleOfPropertyPlantAndEquipmentTable" 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">Property, Plant and Equipment [Table]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ScheduleOfPropertyPlantAndEquipmentTable" xlink:href="http://xbrl.fasb.org/us-gaap/2020/elts/us-gaap-2020-01-31.xsd#us-gaap_ScheduleOfPropertyPlantAndEquipmentTable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ScheduleOfPropertyPlantAndEquipmentTable" xlink:to="lab_us-gaap_ScheduleOfPropertyPlantAndEquipmentTable" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_CashAcquiredFromAcquisition_083267bc-6e8d-4b7f-8e56-b88ca0e3b60d_terseLabel_en-US" xlink:label="lab_us-gaap_CashAcquiredFromAcquisition" 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 Acquired from Acquisition</link:label>
    <link:label id="lab_us-gaap_CashAcquiredFromAcquisition_label_en-US" xlink:label="lab_us-gaap_CashAcquiredFromAcquisition" 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 Acquired from Acquisition</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CashAcquiredFromAcquisition" xlink:href="http://xbrl.fasb.org/us-gaap/2020/elts/us-gaap-2020-01-31.xsd#us-gaap_CashAcquiredFromAcquisition"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_CashAcquiredFromAcquisition" xlink:to="lab_us-gaap_CashAcquiredFromAcquisition" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AccountingPoliciesAbstract_282eaa3f-01cc-42ce-b393-fad01a3425f0_terseLabel_en-US" xlink:label="lab_us-gaap_AccountingPoliciesAbstract" 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">Accounting Policies [Abstract]</link:label>
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    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AccountingPoliciesAbstract" xlink:href="http://xbrl.fasb.org/us-gaap/2020/elts/us-gaap-2020-01-31.xsd#us-gaap_AccountingPoliciesAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AccountingPoliciesAbstract" xlink:to="lab_us-gaap_AccountingPoliciesAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueAfterYearFive_18d509c5-e68d-45b5-af43-20b09ad8f478_terseLabel_en-US" xlink:label="lab_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueAfterYearFive" 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">Thereafter</link:label>
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    <link:label id="lab_codi_RimportsMember_e6377732-1d2d-4ad3-a83e-97c40f36a32d_terseLabel_en-US" xlink:label="lab_codi_RimportsMember" 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">Rimports</link:label>
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    <link:label id="lab_codi_RimportsMember_documentation_en-US" xlink:label="lab_codi_RimportsMember" 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">Rimports [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_codi_RimportsMember" xlink:href="codi-20200930.xsd#codi_RimportsMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_codi_RimportsMember" xlink:to="lab_codi_RimportsMember" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_EntityShellCompany_4bfddbf1-0d23-4e80-9d01-6c4aa8a169db_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>
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    <link:label id="lab_us-gaap_RevenueFromContractWithCustomerExcludingAssessedTax_5d5b3246-d198-44c5-8ca4-c52d85c8d2d4_verboseLabel_en-US" xlink:label="lab_us-gaap_RevenueFromContractWithCustomerExcludingAssessedTax" 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">Net revenues</link:label>
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    <link:label id="lab_us-gaap_ConcentrationRiskPercentage1_f48c642b-a4d0-4ce2-8db5-e6f8eee416ef_terseLabel_en-US" xlink:label="lab_us-gaap_ConcentrationRiskPercentage1" 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">Concentration risk, percentage</link:label>
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    <link:label id="lab_dei_EntityFileNumber_1f4ee49b-ab53-4237-a4b9-02f3e942cc7e_terseLabel_en-US" xlink:label="lab_dei_EntityFileNumber" 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 File Number</link:label>
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    <link:label id="lab_codi_BusinessAcquisitionProFormaGrossProfit_6a90e9f3-fdfe-4eb7-b0a1-1595d3c6c5df_terseLabel_en-US" xlink:label="lab_codi_BusinessAcquisitionProFormaGrossProfit" 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 Acquisition, Pro Forma Gross Profit</link:label>
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    <link:label id="lab_us-gaap_BusinessAcquisitionAxis_b760ccfa-9b50-4ba6-a12a-260be7438e28_terseLabel_en-US" xlink:label="lab_us-gaap_BusinessAcquisitionAxis" 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 Acquisition [Axis]</link:label>
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    <link:label id="lab_srt_SegmentGeographicalDomain_68a35fa5-eb78-4816-859e-d1c69d818794_terseLabel_en-US" xlink:label="lab_srt_SegmentGeographicalDomain" 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">Geographical [Domain]</link:label>
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    <link:label id="lab_us-gaap_StatementLineItems_fc0f34c6-4ce1-4044-ba13-844e83c794b2_terseLabel_en-US" xlink:label="lab_us-gaap_StatementLineItems" 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">Statement [Line Items]</link:label>
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    <link:label id="lab_us-gaap_ClassOfStockDomain_1153bf35-7715-489e-b7c7-62ae8e5ca772_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>
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    <link:label id="lab_us-gaap_OtherNoncurrentAssetsMember_4bd7f50b-68b9-43ad-8c57-a70ea7c53d4f_terseLabel_en-US" xlink:label="lab_us-gaap_OtherNoncurrentAssetsMember" 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 Noncurrent Assets [Member]</link:label>
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    <link:label id="lab_us-gaap_LesseeOperatingLeaseLiabilityUndiscountedExcessAmount_3a234775-189d-4727-be84-ccdbc0da0980_terseLabel_en-US" xlink:label="lab_us-gaap_LesseeOperatingLeaseLiabilityUndiscountedExcessAmount" 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: Interest</link:label>
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    <link:label id="lab_us-gaap_ScenarioAdjustmentMember_57192b89-956e-400a-b92f-a143b56dda28_terseLabel_en-US" xlink:label="lab_us-gaap_ScenarioAdjustmentMember" 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">Scenario, Adjustment</link:label>
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    <link:label id="lab_us-gaap_RevolvingCreditFacilityMember_005de0a6-df01-486a-95da-9fae420a4c08_terseLabel_en-US" xlink:label="lab_us-gaap_RevolvingCreditFacilityMember" 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">Revolving Credit Facility</link:label>
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    <link:label id="lab_us-gaap_EffectiveIncomeTaxRateReconciliationOtherAdjustments_80a8596b-ad4f-424b-86a0-664dfa2fcbc3_terseLabel_en-US" xlink:label="lab_us-gaap_EffectiveIncomeTaxRateReconciliationOtherAdjustments" 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</link:label>
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    <link:label id="lab_us-gaap_LettersOfCreditOutstandingAmount_6b9fe63d-8f81-42ff-be49-9425c2906cfd_terseLabel_en-US" xlink:label="lab_us-gaap_LettersOfCreditOutstandingAmount" 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">Letter of credit outstanding</link:label>
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    <link:label id="lab_us-gaap_PropertyPlantAndEquipmentGross_dca560e9-ca31-4e6f-8909-9ce6e9d6e94e_terseLabel_en-US" xlink:label="lab_us-gaap_PropertyPlantAndEquipmentGross" 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, gross</link:label>
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    <link:label id="lab_us-gaap_IncomeTaxAuthorityAxis_9b62f756-6e12-410c-8209-aefed5d3dfc8_terseLabel_en-US" xlink:label="lab_us-gaap_IncomeTaxAuthorityAxis" 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 Tax Authority [Axis]</link:label>
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    <link:label id="lab_codi_DisposalGroupTotalenterprisevalue_b1a7a3ec-d6b4-4833-a6de-c7a42c4b4bd7_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>
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    <link:label id="lab_codi_DistributionToShareholders_documentation_en-US" xlink:label="lab_codi_DistributionToShareholders" 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 to shareholders.</link:label>
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    <link:label id="lab_us-gaap_AccountsReceivableNetCurrent_7beb2e2e-040a-44fe-a4e9-94a900bf1dd6_terseLabel_en-US" xlink:label="lab_us-gaap_AccountsReceivableNetCurrent" 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, net</link:label>
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    <link:label id="lab_us-gaap_InventoryFinishedGoods_93cc3af8-b342-4b4a-848e-d7aadb39cc7f_terseLabel_en-US" xlink:label="lab_us-gaap_InventoryFinishedGoods" 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">Finished goods</link:label>
    <link:label id="lab_us-gaap_InventoryFinishedGoods_label_en-US" xlink:label="lab_us-gaap_InventoryFinishedGoods" 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">Inventory, Finished Goods, Gross</link:label>
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    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_InventoryFinishedGoods" xlink:to="lab_us-gaap_InventoryFinishedGoods" xlink:type="arc" order="1"/>
    <link:label id="lab_codi_BusinessCombinationStepAcquisitionInventoryRemeasurement_34679fa9-3e66-4aea-879b-28bee7698961_terseLabel_en-US" xlink:label="lab_codi_BusinessCombinationStepAcquisitionInventoryRemeasurement" 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, Step Acquisition, Inventory, Remeasurement</link:label>
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    <link:label id="lab_codi_BusinessCombinationStepAcquisitionInventoryRemeasurement_documentation_en-US" xlink:label="lab_codi_BusinessCombinationStepAcquisitionInventoryRemeasurement" 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">Business Combination, Step Acquisition, Inventory, Remeasurement</link:label>
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    <link:label id="lab_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDue_aa941846-c4cf-4c65-b4a3-759fc1b5e619_totalLabel_en-US" xlink:label="lab_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDue" 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 undiscounted lease payments</link:label>
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    <link:label id="lab_us-gaap_MinorityInterestOwnershipPercentageByParent_7aafcd41-0948-4801-b671-125888df6c14_terseLabel_en-US" xlink:label="lab_us-gaap_MinorityInterestOwnershipPercentageByParent" 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, Ownership Percentage by Parent</link:label>
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    <link:label id="lab_codi_NetIncomeLossAvailableToTrustStockNetOfHoldingEventAdjustment_736dde7c-b252-4533-b261-069b3260a3f5_terseLabel_en-US" xlink:label="lab_codi_NetIncomeLossAvailableToTrustStockNetOfHoldingEventAdjustment" 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 (loss) from continuing operations attributable to common shares of Holdings</link:label>
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    <link:label id="lab_us-gaap_DepreciationAndAmortization_3b860bd3-7283-4f98-9e28-aeaf59877403_terseLabel_en-US" xlink:label="lab_us-gaap_DepreciationAndAmortization" 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 and Amortization Expense</link:label>
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    <link:label id="lab_codi_NumberOfClients_ae0d0d71-be74-4351-97c6-380d8a8b5d41_terseLabel_en-US" xlink:label="lab_codi_NumberOfClients" 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">Number of clients</link:label>
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    <link:label id="lab_us-gaap_BusinessAcquisitionProFormaEarningsPerShareBasic_d33a7581-f0e3-4b96-90ef-355ef3872b15_terseLabel_en-US" xlink:label="lab_us-gaap_BusinessAcquisitionProFormaEarningsPerShareBasic" 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 Acquisition, Pro Forma Earnings Per Share, Basic</link:label>
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    <link:label id="lab_us-gaap_Goodwill_67358606-ed4e-4ece-8953-fbf060e4aff5_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_b8feab2a-6fc5-464b-ac63-05af77743520_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_69ab5771-e708-4caf-a76d-75f920a1e43c_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>
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    <link:label id="lab_codi_OtherInternationalMember_eef27d2f-3f02-442b-bdd0-772b9ce204ff_terseLabel_en-US" xlink:label="lab_codi_OtherInternationalMember" 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 international</link:label>
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    <link:label id="lab_us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedNoncurrentLiabilitiesOther_073bdaf8-62c2-4826-9aec-baafd5cfa9c7_terseLabel_en-US" xlink:label="lab_us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedNoncurrentLiabilitiesOther" 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, Noncurrent Liabilities, Other</link:label>
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    <link:label id="lab_us-gaap_NonoperatingIncomeExpenseAbstract_0d098b34-599d-43ac-ba88-6caad9fb1798_terseLabel_en-US" xlink:label="lab_us-gaap_NonoperatingIncomeExpenseAbstract" 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):</link:label>
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    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_NonoperatingIncomeExpenseAbstract" xlink:to="lab_us-gaap_NonoperatingIncomeExpenseAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_CommonStockDividendsPerShareDeclared_f70a7f08-0297-4ef1-8952-6daf26e3db69_terseLabel_en-US" xlink:label="lab_us-gaap_CommonStockDividendsPerShareDeclared" 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 distributions declared per share (refer to Note J) (usd per share)</link:label>
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    <link:label id="lab_us-gaap_DebtInstrumentFaceAmount_54c5d93a-9ced-4d8a-ada3-bb1924802141_terseLabel_en-US" xlink:label="lab_us-gaap_DebtInstrumentFaceAmount" 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">Credit facility obtained</link:label>
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    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DebtInstrumentFaceAmount" xlink:href="http://xbrl.fasb.org/us-gaap/2020/elts/us-gaap-2020-01-31.xsd#us-gaap_DebtInstrumentFaceAmount"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DebtInstrumentFaceAmount" xlink:to="lab_us-gaap_DebtInstrumentFaceAmount" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FairValueInputsLevel2Member_ec250121-b02b-470b-97cd-9c91a22bd189_terseLabel_en-US" xlink:label="lab_us-gaap_FairValueInputsLevel2Member" 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">Level 2</link:label>
    <link:label id="lab_us-gaap_FairValueInputsLevel2Member_label_en-US" xlink:label="lab_us-gaap_FairValueInputsLevel2Member" 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, Inputs, Level 2 [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FairValueInputsLevel2Member" xlink:href="http://xbrl.fasb.org/us-gaap/2020/elts/us-gaap-2020-01-31.xsd#us-gaap_FairValueInputsLevel2Member"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FairValueInputsLevel2Member" xlink:to="lab_us-gaap_FairValueInputsLevel2Member" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_OperatingLeasesOfLesseeDisclosureTextBlock_e11d0a49-b221-4b0f-8183-e74329212194_terseLabel_en-US" xlink:label="lab_us-gaap_OperatingLeasesOfLesseeDisclosureTextBlock" 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 and Discount Rate For Operating Leases</link:label>
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    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OperatingLeasesOfLesseeDisclosureTextBlock" xlink:href="http://xbrl.fasb.org/us-gaap/2020/elts/us-gaap-2020-01-31.xsd#us-gaap_OperatingLeasesOfLesseeDisclosureTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_OperatingLeasesOfLesseeDisclosureTextBlock" xlink:to="lab_us-gaap_OperatingLeasesOfLesseeDisclosureTextBlock" xlink:type="arc" order="1"/>
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    <link:label id="lab_us-gaap_FairValueAssetsMeasuredOnNonrecurringBasisTextBlock_8b3b22e5-3f0f-4a1e-bc9a-0c9b8b18d608_terseLabel_en-US" xlink:label="lab_us-gaap_FairValueAssetsMeasuredOnNonrecurringBasisTextBlock" 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, Nonrecurring</link:label>
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    <link:label id="lab_us-gaap_ScheduleOfGoodwillTextBlock_3e718539-4ada-4460-857f-f7c177ebb70d_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:label id="lab_codi_AllocationInterestsMember_67cfc392-bb0d-4db3-9bda-2b97f9e20358_terseLabel_en-US" xlink:label="lab_codi_AllocationInterestsMember" 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">Allocation Interests [Member]</link:label>
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    <link:label id="lab_us-gaap_EquityAbstract_d4e8064a-1a18-4723-b5e9-51d0e5e234a0_terseLabel_en-US" xlink:label="lab_us-gaap_EquityAbstract" 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">Equity [Abstract]</link:label>
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    <link:label id="lab_currency_AllCurrenciesDomain_label_en-US" xlink:label="lab_currency_AllCurrenciesDomain" 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">All Currencies [Domain]</link:label>
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    <link:label id="lab_us-gaap_SubsequentEventTable_label_en-US" xlink:label="lab_us-gaap_SubsequentEventTable" 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 Event [Table]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_SubsequentEventTable" xlink:href="http://xbrl.fasb.org/us-gaap/2020/elts/us-gaap-2020-01-31.xsd#us-gaap_SubsequentEventTable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_SubsequentEventTable" xlink:to="lab_us-gaap_SubsequentEventTable" xlink:type="arc" order="1"/>
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    <link:label id="lab_codi_ImpairmentAssessmentAssumptionsWeightedAverageCostOfCapital_documentation_en-US" xlink:label="lab_codi_ImpairmentAssessmentAssumptionsWeightedAverageCostOfCapital" 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">Impairment assessment assumptions weighted average cost of capital.</link:label>
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    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DebtInstrumentTable" xlink:href="http://xbrl.fasb.org/us-gaap/2020/elts/us-gaap-2020-01-31.xsd#us-gaap_DebtInstrumentTable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DebtInstrumentTable" xlink:to="lab_us-gaap_DebtInstrumentTable" xlink:type="arc" order="1"/>
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    <link:label id="lab_us-gaap_MinorityInterest_b43e49f5-05dc-42f2-9bdc-2f027c8cd087_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>
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    <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_IncomeLossFromContinuingOperationsPerBasicAndDilutedShare_5680e315-fd1b-4079-a2a9-39dd2e4c79f2_terseLabel_en-US" xlink:label="lab_us-gaap_IncomeLossFromContinuingOperationsPerBasicAndDilutedShare" 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 and fully diluted income (loss) per share attributable to Holdings, continuing operations (usd per share)</link:label>
    <link:label id="lab_us-gaap_IncomeLossFromContinuingOperationsPerBasicAndDilutedShare_label_en-US" xlink:label="lab_us-gaap_IncomeLossFromContinuingOperationsPerBasicAndDilutedShare" 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, Per Basic and Diluted Share</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_IncomeLossFromContinuingOperationsPerBasicAndDilutedShare" xlink:href="http://xbrl.fasb.org/us-gaap/2020/elts/us-gaap-2020-01-31.xsd#us-gaap_IncomeLossFromContinuingOperationsPerBasicAndDilutedShare"/>
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    <link:label id="lab_us-gaap_FairValueByFairValueHierarchyLevelAxis_645fbc1b-8ac4-410a-b45d-15d11d4c581b_terseLabel_en-US" xlink:label="lab_us-gaap_FairValueByFairValueHierarchyLevelAxis" 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 Hierarchy and NAV [Axis]</link:label>
    <link:label id="lab_us-gaap_FairValueByFairValueHierarchyLevelAxis_label_en-US" xlink:label="lab_us-gaap_FairValueByFairValueHierarchyLevelAxis" 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 Hierarchy and NAV [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FairValueByFairValueHierarchyLevelAxis" xlink:href="http://xbrl.fasb.org/us-gaap/2020/elts/us-gaap-2020-01-31.xsd#us-gaap_FairValueByFairValueHierarchyLevelAxis"/>
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    <link:label id="lab_us-gaap_ReconciliationOfAssetsFromSegmentToConsolidatedTable_ac05ec1e-825b-4363-920b-caabecacfb94_terseLabel_en-US" xlink:label="lab_us-gaap_ReconciliationOfAssetsFromSegmentToConsolidatedTable" 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">Reconciliation of Assets from Segment to Consolidated [Table]</link:label>
    <link:label id="lab_us-gaap_ReconciliationOfAssetsFromSegmentToConsolidatedTable_label_en-US" xlink:label="lab_us-gaap_ReconciliationOfAssetsFromSegmentToConsolidatedTable" 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 Assets from Segment to Consolidated [Table]</link:label>
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    <link:label id="lab_us-gaap_OperatingLeaseCost_547e31e6-4b0e-44de-871e-bae0c1f06379_terseLabel_en-US" xlink:label="lab_us-gaap_OperatingLeaseCost" 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 cost</link:label>
    <link:label id="lab_us-gaap_OperatingLeaseCost_label_en-US" xlink:label="lab_us-gaap_OperatingLeaseCost" 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, Cost</link:label>
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    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_OperatingLeaseCost" xlink:to="lab_us-gaap_OperatingLeaseCost" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ParentMember_06fd7da3-949c-463e-b659-8565bc2cfce0_terseLabel_en-US" xlink:label="lab_us-gaap_ParentMember" 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">Stockholders' Equity Attributable to Holdings</link:label>
    <link:label id="lab_us-gaap_ParentMember_label_en-US" xlink:label="lab_us-gaap_ParentMember" 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">Parent [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ParentMember" xlink:href="http://xbrl.fasb.org/us-gaap/2020/elts/us-gaap-2020-01-31.xsd#us-gaap_ParentMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ParentMember" xlink:to="lab_us-gaap_ParentMember" xlink:type="arc" order="1"/>
    <link:label id="lab_codi_VelocityOutdoorOwnershipMember_89d9b75a-614e-4eb8-8d13-dd8f909d4df3_terseLabel_en-US" xlink:label="lab_codi_VelocityOutdoorOwnershipMember" 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 Outdoor</link:label>
    <link:label id="lab_codi_VelocityOutdoorOwnershipMember_label_en-US" xlink:label="lab_codi_VelocityOutdoorOwnershipMember" 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">Velocity Outdoor Ownership [Member]</link:label>
    <link:label id="lab_codi_VelocityOutdoorOwnershipMember_documentation_en-US" xlink:label="lab_codi_VelocityOutdoorOwnershipMember" 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">Velocity Outdoor Ownership [Member]</link:label>
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    <link:label id="lab_us-gaap_SeriesCPreferredStockMember_2fd9b4ab-ba71-491e-98a3-5068de07d852_terseLabel_en-US" xlink:label="lab_us-gaap_SeriesCPreferredStockMember" 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 C Preferred Stock [Member]</link:label>
    <link:label id="lab_us-gaap_SeriesCPreferredStockMember_label_en-US" xlink:label="lab_us-gaap_SeriesCPreferredStockMember" 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 C Preferred Stock [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_SeriesCPreferredStockMember" xlink:href="http://xbrl.fasb.org/us-gaap/2020/elts/us-gaap-2020-01-31.xsd#us-gaap_SeriesCPreferredStockMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_SeriesCPreferredStockMember" xlink:to="lab_us-gaap_SeriesCPreferredStockMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_OtherNoncashIncomeExpense_62f21663-cfe8-4b78-8dfd-335998eebad9_negatedLabel_en-US" xlink:label="lab_us-gaap_OtherNoncashIncomeExpense" 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</link:label>
    <link:label id="lab_us-gaap_OtherNoncashIncomeExpense_label_en-US" xlink:label="lab_us-gaap_OtherNoncashIncomeExpense" 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 Noncash Income (Expense)</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OtherNoncashIncomeExpense" xlink:href="http://xbrl.fasb.org/us-gaap/2020/elts/us-gaap-2020-01-31.xsd#us-gaap_OtherNoncashIncomeExpense"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_OtherNoncashIncomeExpense" xlink:to="lab_us-gaap_OtherNoncashIncomeExpense" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DiscontinuedOperationsPolicyTextBlock_2c4559a1-b364-41f8-ab01-965ff9c977cc_terseLabel_en-US" xlink:label="lab_us-gaap_DiscontinuedOperationsPolicyTextBlock" 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">Discontinued Operations, Policy [Policy Text Block]</link:label>
    <link:label id="lab_us-gaap_DiscontinuedOperationsPolicyTextBlock_label_en-US" xlink:label="lab_us-gaap_DiscontinuedOperationsPolicyTextBlock" 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">Discontinued Operations, Policy [Policy Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DiscontinuedOperationsPolicyTextBlock" xlink:href="http://xbrl.fasb.org/us-gaap/2020/elts/us-gaap-2020-01-31.xsd#us-gaap_DiscontinuedOperationsPolicyTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DiscontinuedOperationsPolicyTextBlock" xlink:to="lab_us-gaap_DiscontinuedOperationsPolicyTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_IndefiniteLivedIntangibleAssetsByMajorClassAxis_9ec0a321-4de1-4e59-b6b1-1cbeabe5b9d1_terseLabel_en-US" xlink:label="lab_us-gaap_IndefiniteLivedIntangibleAssetsByMajorClassAxis" 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">Indefinite-lived Intangible Assets [Axis]</link:label>
    <link:label id="lab_us-gaap_IndefiniteLivedIntangibleAssetsByMajorClassAxis_label_en-US" xlink:label="lab_us-gaap_IndefiniteLivedIntangibleAssetsByMajorClassAxis" 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">Indefinite-lived Intangible Assets [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_IndefiniteLivedIntangibleAssetsByMajorClassAxis" xlink:href="http://xbrl.fasb.org/us-gaap/2020/elts/us-gaap-2020-01-31.xsd#us-gaap_IndefiniteLivedIntangibleAssetsByMajorClassAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_IndefiniteLivedIntangibleAssetsByMajorClassAxis" xlink:to="lab_us-gaap_IndefiniteLivedIntangibleAssetsByMajorClassAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_EquityComponentDomain_bbe504e5-a344-4737-b3a9-28b3d491e3d5_terseLabel_en-US" xlink:label="lab_us-gaap_EquityComponentDomain" 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">Equity Component [Domain]</link:label>
    <link:label id="lab_us-gaap_EquityComponentDomain_label_en-US" xlink:label="lab_us-gaap_EquityComponentDomain" 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">Equity Component [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_EquityComponentDomain" xlink:href="http://xbrl.fasb.org/us-gaap/2020/elts/us-gaap-2020-01-31.xsd#us-gaap_EquityComponentDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_EquityComponentDomain" xlink:to="lab_us-gaap_EquityComponentDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_EntityAddressAddressLine1_ba21bc50-bdee-49ad-93f5-3e5a7d1152db_terseLabel_en-US" xlink:label="lab_dei_EntityAddressAddressLine1" 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, Address Line One</link:label>
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    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_EntityAddressAddressLine1" xlink:to="lab_dei_EntityAddressAddressLine1" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_EntityAddressAddressLine2_89a4ac06-4e39-4f03-85ea-fe0c837532a3_terseLabel_en-US" xlink:label="lab_dei_EntityAddressAddressLine2" 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, Address Line Two</link:label>
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    <link:label id="lab_us-gaap_GrossProfit_68912ce6-4f59-45a9-93ef-a7931f3193ac_totalLabel_en-US" xlink:label="lab_us-gaap_GrossProfit" 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">Gross profit</link:label>
    <link:label id="lab_us-gaap_GrossProfit_label_en-US" xlink:label="lab_us-gaap_GrossProfit" 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">Gross Profit</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_GrossProfit" xlink:href="http://xbrl.fasb.org/us-gaap/2020/elts/us-gaap-2020-01-31.xsd#us-gaap_GrossProfit"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_GrossProfit" xlink:to="lab_us-gaap_GrossProfit" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_PropertyPlantAndEquipmentNet_5a0c5eb6-443f-4919-ae78-d72756899f5c_terseLabel_en-US" xlink:label="lab_us-gaap_PropertyPlantAndEquipmentNet" 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, net</link:label>
    <link:label id="lab_us-gaap_PropertyPlantAndEquipmentNet_346eeeba-5cd4-4d47-8098-02007ee35dcc_totalLabel_en-US" xlink:label="lab_us-gaap_PropertyPlantAndEquipmentNet" 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</link:label>
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    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_PropertyPlantAndEquipmentNet" xlink:to="lab_us-gaap_PropertyPlantAndEquipmentNet" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseYearThree_53627c38-6b1d-4863-9e68-4110fe647070_terseLabel_en-US" xlink:label="lab_us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseYearThree" 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">2020</link:label>
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    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseYearThree" xlink:to="lab_us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseYearThree" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_InterestIncomeExpenseNonoperatingNet_8f26a086-ddfc-4e13-84b4-ec9782cf5163_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:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_InterestIncomeExpenseNonoperatingNet" xlink:to="lab_us-gaap_InterestIncomeExpenseNonoperatingNet" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_NetIncomeLoss_395691f9-6964-4a65-86d0-65038190d209_totalLabel_en-US" xlink:label="lab_us-gaap_NetIncomeLoss" 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 income (loss) attributable to Holdings</link:label>
    <link:label id="lab_us-gaap_NetIncomeLoss_b2841c5d-f355-4b4b-8e8a-783d050e0f42_terseLabel_en-US" xlink:label="lab_us-gaap_NetIncomeLoss" 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 loss attributable to Holdings</link:label>
    <link:label id="lab_us-gaap_NetIncomeLoss_label_en-US" xlink:label="lab_us-gaap_NetIncomeLoss" 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) Attributable to Parent</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_NetIncomeLoss" xlink:href="http://xbrl.fasb.org/us-gaap/2020/elts/us-gaap-2020-01-31.xsd#us-gaap_NetIncomeLoss"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_NetIncomeLoss" xlink:to="lab_us-gaap_NetIncomeLoss" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_EntityAddressStateOrProvince_4f349fd5-4700-486a-afc5-2aa0ec82705a_terseLabel_en-US" xlink:label="lab_dei_EntityAddressStateOrProvince" 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, State or Province</link:label>
    <link:label id="lab_dei_EntityAddressStateOrProvince_label_en-US" xlink:label="lab_dei_EntityAddressStateOrProvince" 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, State or Province</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_EntityAddressStateOrProvince" xlink:href="https://xbrl.sec.gov/dei/2019/dei-2019-01-31.xsd#dei_EntityAddressStateOrProvince"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_EntityAddressStateOrProvince" xlink:to="lab_dei_EntityAddressStateOrProvince" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_IncreaseDecreaseInOperatingCapitalAbstract_e7f3f23c-a48f-4daf-bb1d-3a22394bd1e9_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>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_IncreaseDecreaseInOperatingCapitalAbstract" xlink:href="http://xbrl.fasb.org/us-gaap/2020/elts/us-gaap-2020-01-31.xsd#us-gaap_IncreaseDecreaseInOperatingCapitalAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_IncreaseDecreaseInOperatingCapitalAbstract" xlink:to="lab_us-gaap_IncreaseDecreaseInOperatingCapitalAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_OtherLiabilitiesCurrent_aa108b26-7847-42e5-bcfb-04a067724878_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>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OtherLiabilitiesCurrent" xlink:href="http://xbrl.fasb.org/us-gaap/2020/elts/us-gaap-2020-01-31.xsd#us-gaap_OtherLiabilitiesCurrent"/>
    <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"/>
    <link:label id="lab_us-gaap_LesseeOperatingLeaseLiabilityPaymentsRemainderOfFiscalYear_81002781-167f-4d8c-8db7-3ce442404d0f_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>
    <link:label id="lab_us-gaap_LesseeOperatingLeaseLiabilityPaymentsRemainderOfFiscalYear_label_en-US" xlink:label="lab_us-gaap_LesseeOperatingLeaseLiabilityPaymentsRemainderOfFiscalYear" 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">Lessee, Operating Lease, Liability, to be Paid, Remainder of Fiscal Year</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LesseeOperatingLeaseLiabilityPaymentsRemainderOfFiscalYear" xlink:href="http://xbrl.fasb.org/us-gaap/2020/elts/us-gaap-2020-01-31.xsd#us-gaap_LesseeOperatingLeaseLiabilityPaymentsRemainderOfFiscalYear"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LesseeOperatingLeaseLiabilityPaymentsRemainderOfFiscalYear" xlink:to="lab_us-gaap_LesseeOperatingLeaseLiabilityPaymentsRemainderOfFiscalYear" xlink:type="arc" order="1"/>
    <link:label id="lab_codi_DebtInstrumentOriginalIssueDiscountRate_0b8a7695-3a3e-4961-96cf-bdab8d5f1f04_terseLabel_en-US" xlink:label="lab_codi_DebtInstrumentOriginalIssueDiscountRate" 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">Original issue discount</link:label>
    <link:label id="lab_codi_DebtInstrumentOriginalIssueDiscountRate_label_en-US" xlink:label="lab_codi_DebtInstrumentOriginalIssueDiscountRate" 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 Instrument, Original Issue Discount Rate</link:label>
    <link:label id="lab_codi_DebtInstrumentOriginalIssueDiscountRate_documentation_en-US" xlink:label="lab_codi_DebtInstrumentOriginalIssueDiscountRate" 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 Instrument, Original issue discount rate.</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_codi_DebtInstrumentOriginalIssueDiscountRate" xlink:href="codi-20200930.xsd#codi_DebtInstrumentOriginalIssueDiscountRate"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_codi_DebtInstrumentOriginalIssueDiscountRate" xlink:to="lab_codi_DebtInstrumentOriginalIssueDiscountRate" xlink:type="arc" order="1"/>
    <link:label id="lab_srt_EquityMethodInvesteeNameDomain_81aa3abd-6eb4-4d39-88d9-a9d3e09676e6_terseLabel_en-US" xlink:label="lab_srt_EquityMethodInvesteeNameDomain" 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 [Domain]</link:label>
    <link:label id="lab_srt_EquityMethodInvesteeNameDomain_label_en-US" xlink:label="lab_srt_EquityMethodInvesteeNameDomain" 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 [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_srt_EquityMethodInvesteeNameDomain" xlink:href="http://xbrl.fasb.org/srt/2020/elts/srt-2020-01-31.xsd#srt_EquityMethodInvesteeNameDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_srt_EquityMethodInvesteeNameDomain" xlink:to="lab_srt_EquityMethodInvesteeNameDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_codi_ManufacturingFacilityArea_e5b61135-6d97-4367-8179-8477806dec20_terseLabel_en-US" xlink:label="lab_codi_ManufacturingFacilityArea" 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">Manufacturing facility area (in square feet)</link:label>
    <link:label id="lab_codi_ManufacturingFacilityArea_label_en-US" xlink:label="lab_codi_ManufacturingFacilityArea" 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">Manufacturing Facility Area</link:label>
    <link:label id="lab_codi_ManufacturingFacilityArea_documentation_en-US" xlink:label="lab_codi_ManufacturingFacilityArea" 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">Manufacturing facility area.</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_codi_ManufacturingFacilityArea" xlink:href="codi-20200930.xsd#codi_ManufacturingFacilityArea"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_codi_ManufacturingFacilityArea" xlink:to="lab_codi_ManufacturingFacilityArea" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_OtherOwnershipInterestsByNameAxis_8e95bed3-d521-42dc-b7b3-9ed87c35994f_terseLabel_en-US" xlink:label="lab_us-gaap_OtherOwnershipInterestsByNameAxis" 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 [Axis]</link:label>
    <link:label id="lab_us-gaap_OtherOwnershipInterestsByNameAxis_label_en-US" xlink:label="lab_us-gaap_OtherOwnershipInterestsByNameAxis" 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 Ownership Interests Name [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OtherOwnershipInterestsByNameAxis" xlink:href="http://xbrl.fasb.org/us-gaap/2020/elts/us-gaap-2020-01-31.xsd#us-gaap_OtherOwnershipInterestsByNameAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_OtherOwnershipInterestsByNameAxis" xlink:to="lab_us-gaap_OtherOwnershipInterestsByNameAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DebtInstrumentUnamortizedPremium_69feefe8-5605-41f5-9d97-3bd57c0762e4_terseLabel_en-US" xlink:label="lab_us-gaap_DebtInstrumentUnamortizedPremium" 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 Instrument, Unamortized Premium</link:label>
    <link:label id="lab_us-gaap_DebtInstrumentUnamortizedPremium_label_en-US" xlink:label="lab_us-gaap_DebtInstrumentUnamortizedPremium" 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 Instrument, Unamortized Premium</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DebtInstrumentUnamortizedPremium" xlink:href="http://xbrl.fasb.org/us-gaap/2020/elts/us-gaap-2020-01-31.xsd#us-gaap_DebtInstrumentUnamortizedPremium"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DebtInstrumentUnamortizedPremium" xlink:to="lab_us-gaap_DebtInstrumentUnamortizedPremium" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_InventoryWorkInProcess_9359120a-0a66-401f-b293-07b49c30cd2f_terseLabel_en-US" xlink:label="lab_us-gaap_InventoryWorkInProcess" 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">Work-in-process</link:label>
    <link:label id="lab_us-gaap_InventoryWorkInProcess_label_en-US" xlink:label="lab_us-gaap_InventoryWorkInProcess" 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">Inventory, Work in Process, Gross</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_InventoryWorkInProcess" xlink:href="http://xbrl.fasb.org/us-gaap/2020/elts/us-gaap-2020-01-31.xsd#us-gaap_InventoryWorkInProcess"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_InventoryWorkInProcess" xlink:to="lab_us-gaap_InventoryWorkInProcess" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_TradeNamesMember_d22b1331-3078-4e14-8fb2-ca297fa3de12_terseLabel_en-US" xlink:label="lab_us-gaap_TradeNamesMember" 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">Trade name</link:label>
    <link:label id="lab_us-gaap_TradeNamesMember_02a4e531-cc1b-407b-aea9-2fcc98ae59c1_verboseLabel_en-US" xlink:label="lab_us-gaap_TradeNamesMember" 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">Trade Names [Member]</link:label>
    <link:label id="lab_us-gaap_TradeNamesMember_label_en-US" xlink:label="lab_us-gaap_TradeNamesMember" 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">Trade Names [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_TradeNamesMember" xlink:href="http://xbrl.fasb.org/us-gaap/2020/elts/us-gaap-2020-01-31.xsd#us-gaap_TradeNamesMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_TradeNamesMember" xlink:to="lab_us-gaap_TradeNamesMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LeasesAbstract_ee58fece-063c-4ece-8dc1-d799b85c1c8c_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>
    <link:label id="lab_us-gaap_LeasesAbstract_label_en-US" xlink:label="lab_us-gaap_LeasesAbstract" 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">Leases [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LeasesAbstract" xlink:href="http://xbrl.fasb.org/us-gaap/2020/elts/us-gaap-2020-01-31.xsd#us-gaap_LeasesAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LeasesAbstract" xlink:to="lab_us-gaap_LeasesAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LongtermDebtTypeAxis_b1142136-45da-465f-99c6-066be3b562db_terseLabel_en-US" xlink:label="lab_us-gaap_LongtermDebtTypeAxis" 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 [Axis]</link:label>
    <link:label id="lab_us-gaap_LongtermDebtTypeAxis_label_en-US" xlink:label="lab_us-gaap_LongtermDebtTypeAxis" 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 [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LongtermDebtTypeAxis" xlink:href="http://xbrl.fasb.org/us-gaap/2020/elts/us-gaap-2020-01-31.xsd#us-gaap_LongtermDebtTypeAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LongtermDebtTypeAxis" xlink:to="lab_us-gaap_LongtermDebtTypeAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AssetsCurrent_114086d9-5874-4c96-8656-604ee9292d2a_totalLabel_en-US" xlink:label="lab_us-gaap_AssetsCurrent" 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 assets</link:label>
    <link:label id="lab_us-gaap_AssetsCurrent_label_en-US" xlink:label="lab_us-gaap_AssetsCurrent" 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">Assets, Current</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AssetsCurrent" xlink:href="http://xbrl.fasb.org/us-gaap/2020/elts/us-gaap-2020-01-31.xsd#us-gaap_AssetsCurrent"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AssetsCurrent" xlink:to="lab_us-gaap_AssetsCurrent" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_CorporateAndOtherMember_9531396d-77f0-42e0-82e1-41d5fd87f000_terseLabel_en-US" xlink:label="lab_us-gaap_CorporateAndOtherMember" 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">Corporate and other</link:label>
    <link:label id="lab_us-gaap_CorporateAndOtherMember_label_en-US" xlink:label="lab_us-gaap_CorporateAndOtherMember" 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">Corporate and Other [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CorporateAndOtherMember" xlink:href="http://xbrl.fasb.org/us-gaap/2020/elts/us-gaap-2020-01-31.xsd#us-gaap_CorporateAndOtherMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_CorporateAndOtherMember" xlink:to="lab_us-gaap_CorporateAndOtherMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_OperatingExpensesAbstract_7b8a570e-6bde-4bb8-a90a-ed7a1da52fe2_terseLabel_en-US" xlink:label="lab_us-gaap_OperatingExpensesAbstract" 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 expenses:</link:label>
    <link:label id="lab_us-gaap_OperatingExpensesAbstract_label_en-US" xlink:label="lab_us-gaap_OperatingExpensesAbstract" 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 Expenses [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OperatingExpensesAbstract" xlink:href="http://xbrl.fasb.org/us-gaap/2020/elts/us-gaap-2020-01-31.xsd#us-gaap_OperatingExpensesAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_OperatingExpensesAbstract" xlink:to="lab_us-gaap_OperatingExpensesAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_IncomeTaxAuthorityNameAxis_3bff3649-a3b1-43f6-9836-4054798a8ce0_terseLabel_en-US" xlink:label="lab_us-gaap_IncomeTaxAuthorityNameAxis" 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 Tax Authority, Name [Axis]</link:label>
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    <link:label id="lab_us-gaap_CommonStockMember_05f39520-57e2-4131-aa34-5326adb9209e_terseLabel_en-US" xlink:label="lab_us-gaap_CommonStockMember" 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">Trust Common Shares</link:label>
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    <link:label id="lab_us-gaap_PropertyPlantAndEquipmentLineItems_2acde58c-4867-4807-8fe1-86c64cc4daf9_terseLabel_en-US" xlink:label="lab_us-gaap_PropertyPlantAndEquipmentLineItems" 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 [Line Items]</link:label>
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    <link:label id="lab_srt_ProductsAndServicesDomain_be6b8acd-875c-416b-b3c0-d852bdd0c0bd_terseLabel_en-US" xlink:label="lab_srt_ProductsAndServicesDomain" 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">Product and Service [Domain]</link:label>
    <link:label id="lab_srt_ProductsAndServicesDomain_label_en-US" xlink:label="lab_srt_ProductsAndServicesDomain" 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">Product and Service [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_srt_ProductsAndServicesDomain" xlink:href="http://xbrl.fasb.org/srt/2020/elts/srt-2020-01-31.xsd#srt_ProductsAndServicesDomain"/>
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    <link:label id="lab_us-gaap_PropertyPlantAndEquipmentTypeDomain_7620e101-7a10-4b99-8b36-6f62d2c7c7ac_terseLabel_en-US" xlink:label="lab_us-gaap_PropertyPlantAndEquipmentTypeDomain" 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-Lived Tangible Asset [Domain]</link:label>
    <link:label id="lab_us-gaap_PropertyPlantAndEquipmentTypeDomain_label_en-US" xlink:label="lab_us-gaap_PropertyPlantAndEquipmentTypeDomain" 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-Lived Tangible Asset [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PropertyPlantAndEquipmentTypeDomain" xlink:href="http://xbrl.fasb.org/us-gaap/2020/elts/us-gaap-2020-01-31.xsd#us-gaap_PropertyPlantAndEquipmentTypeDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_PropertyPlantAndEquipmentTypeDomain" xlink:to="lab_us-gaap_PropertyPlantAndEquipmentTypeDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_codi_ExpensesOfParentTaxedAsPartnershipPassedThroughToShareholders_d898c2e4-c5b5-4f68-a143-6eb57040e61e_terseLabel_en-US" xlink:label="lab_codi_ExpensesOfParentTaxedAsPartnershipPassedThroughToShareholders" 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">Expenses of Compass Group Diversified Holdings, LLC representing a pass through to shareholders</link:label>
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    <link:label id="lab_us-gaap_NotesReceivableRelatedParties_9928827a-8307-4522-892b-6aed0d29b53c_terseLabel_en-US" xlink:label="lab_us-gaap_NotesReceivableRelatedParties" 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">Notes Receivable, Related Parties</link:label>
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    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_NotesReceivableRelatedParties" xlink:href="http://xbrl.fasb.org/us-gaap/2020/elts/us-gaap-2020-01-31.xsd#us-gaap_NotesReceivableRelatedParties"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_NotesReceivableRelatedParties" xlink:to="lab_us-gaap_NotesReceivableRelatedParties" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_PreferredClassBMember_4c6e7c9c-c3dd-4419-9b63-248abeb17494_terseLabel_en-US" xlink:label="lab_us-gaap_PreferredClassBMember" 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</link:label>
    <link:label id="lab_us-gaap_PreferredClassBMember_label_en-US" xlink:label="lab_us-gaap_PreferredClassBMember" 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 Class B [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PreferredClassBMember" xlink:href="http://xbrl.fasb.org/us-gaap/2020/elts/us-gaap-2020-01-31.xsd#us-gaap_PreferredClassBMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_PreferredClassBMember" xlink:to="lab_us-gaap_PreferredClassBMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisLiabilityGainLossIncludedInOtherComprehensiveIncome_44582bde-8124-4882-aad3-e39176dcc24a_negatedLabel_en-US" xlink:label="lab_us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisLiabilityGainLossIncludedInOtherComprehensiveIncome" 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">Contingent consideration - Rimports (1)</link:label>
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    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisLiabilityGainLossIncludedInOtherComprehensiveIncome" xlink:href="http://xbrl.fasb.org/us-gaap/2020/elts/us-gaap-2020-01-31.xsd#us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisLiabilityGainLossIncludedInOtherComprehensiveIncome"/>
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    <link:label id="lab_codi_PercentageOwnershipFullyDilutedMember_af0a5ea5-b5ea-429d-b01b-724cbd24185f_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_TechnologyBasedIntangibleAssetsMember_14e3b864-76db-437f-aefa-b946f1b68596_terseLabel_en-US" xlink:label="lab_us-gaap_TechnologyBasedIntangibleAssetsMember" 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">Technology-Based Intangible Assets [Member]</link:label>
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    <link:label id="lab_us-gaap_PropertyPlantAndEquipmentTextBlock_9726f522-71fa-4c77-a250-60bfc118c0ef_terseLabel_en-US" xlink:label="lab_us-gaap_PropertyPlantAndEquipmentTextBlock" 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 Property, Plant and Equipment</link:label>
    <link:label id="lab_us-gaap_PropertyPlantAndEquipmentTextBlock_label_en-US" xlink:label="lab_us-gaap_PropertyPlantAndEquipmentTextBlock" 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">Property, Plant and Equipment [Table Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PropertyPlantAndEquipmentTextBlock" xlink:href="http://xbrl.fasb.org/us-gaap/2020/elts/us-gaap-2020-01-31.xsd#us-gaap_PropertyPlantAndEquipmentTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_PropertyPlantAndEquipmentTextBlock" xlink:to="lab_us-gaap_PropertyPlantAndEquipmentTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_PreferredStockDividendRatePercentage_e71158e7-0dcd-4fe7-abf9-73515237c374_terseLabel_en-US" xlink:label="lab_us-gaap_PreferredStockDividendRatePercentage" 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, Dividend Rate, Percentage</link:label>
    <link:label id="lab_us-gaap_PreferredStockDividendRatePercentage_label_en-US" xlink:label="lab_us-gaap_PreferredStockDividendRatePercentage" 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, Dividend Rate, Percentage</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PreferredStockDividendRatePercentage" xlink:href="http://xbrl.fasb.org/us-gaap/2020/elts/us-gaap-2020-01-31.xsd#us-gaap_PreferredStockDividendRatePercentage"/>
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    <link:label id="lab_codi_PropertyPlantAndEquipmentAndInventoryTextBlock_fb54646c-31e4-48e0-8fdf-9d65a7381b8e_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_codi_PropertyPlantAndEquipmentAndInventoryTextBlock_documentation_en-US" xlink:label="lab_codi_PropertyPlantAndEquipmentAndInventoryTextBlock" 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">Property, plant and equipment and inventory.</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_codi_PropertyPlantAndEquipmentAndInventoryTextBlock" xlink:href="codi-20200930.xsd#codi_PropertyPlantAndEquipmentAndInventoryTextBlock"/>
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    <link:label id="lab_us-gaap_LeaseholdImprovementsMember_594f1f89-d429-4ab6-bae2-d9ac4f7acc41_terseLabel_en-US" xlink:label="lab_us-gaap_LeaseholdImprovementsMember" 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">Leasehold improvements</link:label>
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    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LeaseholdImprovementsMember" xlink:href="http://xbrl.fasb.org/us-gaap/2020/elts/us-gaap-2020-01-31.xsd#us-gaap_LeaseholdImprovementsMember"/>
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    <link:label id="lab_us-gaap_FiniteLivedIntangibleAssetsGross_04ab3087-4182-41fd-9f95-940400c20d35_terseLabel_en-US" xlink:label="lab_us-gaap_FiniteLivedIntangibleAssetsGross" 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 intangible assets, gross</link:label>
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