Income Taxes - Reconciliation between Federal Statutory Rate and Effective Income Tax Rate (Detail)	3 Months Ended
Mar. 31, 2024	Mar. 31, 2023
Income Tax Contingency [Line Items]
United States Federal Statutory Rate	21.00%	21.00%
State income taxes (net of Federal benefits)	13.10%	0.10%
Effective Income Tax Rate Reconciliation, Foreign Income Tax Rate Differential, Percent	9.60%	20.20%
Effective Income Tax Rate Reconciliation, Nondeductible Expense, Share-Based Payment Arrangement, Amount	1.70%	(2.30%)
Utilization of tax credits	(20.60%)	(4.00%)
Effective Income Tax Rate Reconciliation, Non Recognition Of Nol Carry Forwards at Subsidiaries	35.50%	30.60%
Effective Income Tax Rate Reconciliation, Repatriation of Foreign Earnings, Percent	(0.90%)	10.10%
Effective Income Tax Rate Reconciliation, Nondeductible Expense, Impairment Losses, Percent	13.40%	0.00%
Other	2.30%	5.40%
Effective income tax rate	78.10%	81.10%
Effective Income Tax Rate Reconciliation, Nondeductible Expense, Percent	3.00%	0.00%

Effective Income Tax Rate Reconciliation, Non Recognition Of Nol Carry Forwards at Subsidiaries

No definition available.

Name:	codi_EffectiveIncomeTaxRateReconciliationNonRecognitionOfNolCarryForwardsAtSubsidiaries
Namespace Prefix:	codi_
Data Type:	dtr-types1:percentItemType
Balance Type:	na
Period Type:	duration

- Definition

Percentage of current income tax expense (benefit) and deferred income tax expense (benefit) pertaining to continuing operations.

+ References

Reference 1: http://www.xbrl.org/2003/role/disclosureRef
-Topic 740
-SubTopic 10
-Name Accounting Standards Codification
-Section 50
-Paragraph 12
-Publisher FASB
-URI https://asc.fasb.org//1943274/2147482685/740-10-50-12

+ Details

Name:	us-gaap_EffectiveIncomeTaxRateContinuingOperations
Namespace Prefix:	us-gaap_
Data Type:	dtr-types:percentItemType
Balance Type:	na
Period Type:	duration

- Definition

Percentage of domestic federal statutory tax rate applicable to pretax income (loss).

+ References

Reference 1: http://www.xbrl.org/2003/role/disclosureRef
-Topic 235
-SubTopic 10
-Name Accounting Standards Codification
-Section S99
-Paragraph 1
-Subparagraph (SX 210.4-08(h)(2))
-Publisher FASB
-URI https://asc.fasb.org//1943274/2147480678/235-10-S99-1

Reference 2: http://www.xbrl.org/2003/role/disclosureRef
-Topic 740
-SubTopic 10
-Name Accounting Standards Codification
-Section 50
-Paragraph 12
-Publisher FASB
-URI https://asc.fasb.org//1943274/2147482685/740-10-50-12

Reference 3: http://www.xbrl.org/2003/role/disclosureRef
-Topic 740
-SubTopic 10
-Name Accounting Standards Codification
-Section S99
-Paragraph 1
-Subparagraph (SAB Topic 6.I.Fact.4)
-Publisher FASB
-URI https://asc.fasb.org//1943274/2147479360/740-10-S99-1

+ Details

Name:	us-gaap_EffectiveIncomeTaxRateReconciliationAtFederalStatutoryIncomeTaxRate
Namespace Prefix:	us-gaap_
Data Type:	dtr-types:percentItemType
Balance Type:	na
Period Type:	duration

- Definition

Percentage of the difference between reported income tax expense (benefit) and expected income tax expense (benefit) computed by applying the domestic federal statutory income tax rates to pretax income (loss) from continuing operations applicable to statutory income tax expense (benefit) outside of the country of domicile.

+ References

Reference 1: http://www.xbrl.org/2009/role/commonPracticeRef
-Topic 740
-SubTopic 10
-Name Accounting Standards Codification
-Section 50
-Paragraph 12
-Publisher FASB
-URI https://asc.fasb.org//1943274/2147482685/740-10-50-12

Reference 2: http://www.xbrl.org/2009/role/commonPracticeRef
-Topic 740
-SubTopic 10
-Name Accounting Standards Codification
-Section S99
-Paragraph 1
-Subparagraph (SAB Topic 6.I.Fact.4)
-Publisher FASB
-URI https://asc.fasb.org//1943274/2147479360/740-10-S99-1

+ Details

Name:	us-gaap_EffectiveIncomeTaxRateReconciliationForeignIncomeTaxRateDifferential
Namespace Prefix:	us-gaap_
Data Type:	dtr-types:percentItemType
Balance Type:	na
Period Type:	duration

- Definition

+ References

+ Details

Name:	us-gaap_EffectiveIncomeTaxRateReconciliationNondeductibleExpense
Namespace Prefix:	us-gaap_
Data Type:	dtr-types:percentItemType
Balance Type:	na
Period Type:	duration

- Definition

+ References

+ Details

Name:	us-gaap_EffectiveIncomeTaxRateReconciliationNondeductibleExpenseImpairmentLosses
Namespace Prefix:	us-gaap_
Data Type:	dtr-types:percentItemType
Balance Type:	na
Period Type:	duration

- Definition

Percentage of difference between reported income tax expense (benefit) and expected income tax expense (benefit) computed by applying domestic federal statutory income tax rate to pretax income (loss) from continuing operation, attributable to nondeductible expense for share-based payment arrangement.

+ References

+ Details

Name:	us-gaap_EffectiveIncomeTaxRateReconciliationNondeductibleExpenseShareBasedCompensationCost
Namespace Prefix:	us-gaap_
Data Type:	dtr-types:percentItemType
Balance Type:	na
Period Type:	duration

- Definition

+ References

+ Details

Name:	us-gaap_EffectiveIncomeTaxRateReconciliationOtherAdjustments
Namespace Prefix:	us-gaap_
Data Type:	dtr-types:percentItemType
Balance Type:	na
Period Type:	duration

- Definition

Percentage of the difference between reported income tax expense (benefit) and expected income tax expense (benefit) computed by applying the domestic federal statutory income tax rates to pretax income (loss) from continuing operations attributable to the repatriation of foreign earnings.

+ References

+ Details

Name:	us-gaap_EffectiveIncomeTaxRateReconciliationRepatriationOfForeignEarnings
Namespace Prefix:	us-gaap_
Data Type:	dtr-types:percentItemType
Balance Type:	na
Period Type:	duration

- Definition

Percentage of the difference between reported income tax expense (benefit) and expected income tax expense (benefit) computed by applying the domestic federal statutory income tax rates to pretax income (loss) from continuing operations applicable to state and local income tax expense (benefit), net of federal tax expense (benefit).

+ References

+ Details

Name:	us-gaap_EffectiveIncomeTaxRateReconciliationStateAndLocalIncomeTaxes
Namespace Prefix:	us-gaap_
Data Type:	dtr-types:percentItemType
Balance Type:	na
Period Type:	duration

- Definition

Percentage of the difference between reported income tax expense (benefit) and expected income tax expense (benefit) computed by applying the domestic federal statutory income tax rates to pretax income (loss) from continuing operations attributable to tax credits. Including, but not limited to, research credit, foreign tax credit, investment tax credit, and other tax credits.

+ References

+ Details

Name:	us-gaap_EffectiveIncomeTaxRateReconciliationTaxCredits
Namespace Prefix:	us-gaap_
Data Type:	dtr-types:percentItemType
Balance Type:	na
Period Type:	duration

- Definition

Line items represent financial concepts included in a table. These concepts are used to disclose reportable information associated with domain members defined in one or many axes to the table.

+ References

No definition available.

+ Details

Name:	us-gaap_IncomeTaxContingencyLineItems
Namespace Prefix:	us-gaap_
Data Type:	xbrli:stringItemType
Balance Type:	na
Period Type:	duration