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Stockholders' Equity - Additional Information (Detail) (USD $)
3 Months Ended 12 Months Ended
Jun. 30, 2013
Mar. 31, 2013
Dec. 31, 2014
Dec. 31, 2013
Dec. 31, 2012
Share Based Compensation Arrangement By Share Based Payment Award [Line Items]          
Treasury stock purchases     0us-gaap_TreasuryStockSharesAcquired 0us-gaap_TreasuryStockSharesAcquired 0us-gaap_TreasuryStockSharesAcquired
Shares available for purchase     678,000us-gaap_StockRepurchaseProgramNumberOfSharesAuthorizedToBeRepurchased    
Common Stock Dividend declared by directors $ 0.05us-gaap_CommonStockDividendsPerShareDeclared $ 0.125us-gaap_CommonStockDividendsPerShareDeclared      
2013 Director Stock Plan          
Share Based Compensation Arrangement By Share Based Payment Award [Line Items]          
Common stock shares authorized to be issued under the plan     200,000us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardNumberOfAdditionalSharesAuthorized
/ us-gaap_PlanNameAxis
= cix_IncentiveCompensationPlanMember
   
Shares available for award     188,000us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardNumberOfSharesAvailableForGrant
/ us-gaap_PlanNameAxis
= cix_IncentiveCompensationPlanMember
   
Class A Common Stock          
Share Based Compensation Arrangement By Share Based Payment Award [Line Items]          
Common stock, vote per share     1cix_CommonStockNumberOfVotes
/ us-gaap_StatementClassOfStockAxis
= us-gaap_CommonClassAMember
   
Class B Common Stock | NL | All Matters Except Election Of Directors          
Share Based Compensation Arrangement By Share Based Payment Award [Line Items]          
Common stock, vote per share     1cix_CommonStockNumberOfVotes
/ us-gaap_RelatedPartyTransactionsByRelatedPartyAxis
= cix_NlIndustriesMember
/ us-gaap_StatementClassOfStockAxis
= us-gaap_CommonClassBMember
/ us-gaap_StatementScenarioAxis
= cix_AllMattersExceptElectionOfDirectorsMember
   
Class B Common Stock | NL | Election Of Directors          
Share Based Compensation Arrangement By Share Based Payment Award [Line Items]          
Common stock, vote per share     10cix_CommonStockNumberOfVotes
/ us-gaap_RelatedPartyTransactionsByRelatedPartyAxis
= cix_NlIndustriesMember
/ us-gaap_StatementClassOfStockAxis
= us-gaap_CommonClassBMember
/ us-gaap_StatementScenarioAxis
= cix_ElectionOfDirectorsMember