Note 6 - Accrued Expenses - Schedule of Accrued Expenses (Details) - USD ($) $ in Thousands	Jun. 30, 2022	Dec. 31, 2021
Compensation and benefits	$ 845	$ 1,601
Project expenses	1,651	704
Accrued milestone	0	6,000
Marketable securities not settled	513	0
Other	292	470
Total accrued expenses	$ 3,301	$ 8,775

Amount of accrued milestone classified as current.

No definition available.

Name:	cmpx_AccruedMilestoneCurrent
Namespace Prefix:	cmpx_
Data Type:	xbrli:monetaryItemType
Balance Type:	credit
Period Type:	instant

- Definition

Amount of accrued project expenses classified as current.

+ References

No definition available.

+ Details

Name:	cmpx_AccruedProjectExpensesCurrent
Namespace Prefix:	cmpx_
Data Type:	xbrli:monetaryItemType
Balance Type:	credit
Period Type:	instant

- Definition

Represents current marketable securities not settlement.

+ References

No definition available.

+ Details

Name:	cmpx_MarketableSecuritiesNotSettlementCurrent
Namespace Prefix:	cmpx_
Data Type:	xbrli:monetaryItemType
Balance Type:	credit
Period Type:	instant

- Definition

Carrying value as of the balance sheet date of obligations, excluding pension and other postretirement benefits, incurred through that date and payable for perquisites provided to employees pertaining to services received from them. Used to reflect the current portion of the liabilities (due within one year or within the normal operating cycle if longer).

+ References

Reference 1: http://fasb.org/us-gaap/role/ref/legacyRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 210
-SubTopic 10
-Section S99
-Paragraph 1
-Subparagraph (SX 210.5-02.20)
-URI https://asc.fasb.org/extlink&oid=120391452&loc=d3e13212-122682

+ Details

Name:	us-gaap_AccruedEmployeeBenefitsCurrent
Namespace Prefix:	us-gaap_
Data Type:	xbrli:monetaryItemType
Balance Type:	credit
Period Type:	instant

- Definition

Carrying value as of the balance sheet date of obligations incurred and payable, pertaining to costs that are statutory in nature, are incurred on contractual obligations, or accumulate over time and for which invoices have not yet been received or will not be rendered. Examples include taxes, interest, rent and utilities. Used to reflect the current portion of the liabilities (due within one year or within the normal operating cycle if longer).

+ References

+ Details

Name:	us-gaap_AccruedLiabilitiesCurrent
Namespace Prefix:	us-gaap_
Data Type:	xbrli:monetaryItemType
Balance Type:	credit
Period Type:	instant

- Definition

Amount of expenses incurred but not yet paid classified as other, due within one year or the normal operating cycle, if longer.

+ References

+ Details

Name:	us-gaap_OtherAccruedLiabilitiesCurrent
Namespace Prefix:	us-gaap_
Data Type:	xbrli:monetaryItemType
Balance Type:	credit
Period Type:	instant