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Pension and Postretirement Plans Pension and Postretirement Assumptions (Details) (USD $)
In Millions, unless otherwise specified
12 Months Ended
Dec. 31, 2014
Dec. 31, 2013
Dec. 31, 2012
Defined Benefit Plan, Assumed Health Care Cost Trend Rates [Abstract]      
Healthcare cost trend 6.50%us-gaap_DefinedBenefitPlanHealthCareCostTrendRateAssumedForNextFiscalYear 6.50%us-gaap_DefinedBenefitPlanHealthCareCostTrendRateAssumedForNextFiscalYear  
Rate to which the cost trend is assumed to decline (ultimate trend rate) 4.50%us-gaap_DefinedBenefitPlanUltimateHealthCareCostTrendRate 4.50%us-gaap_DefinedBenefitPlanUltimateHealthCareCostTrendRate  
Year the rates reach the ultimate trend rate 2018 2017  
Defined Benefit Plan, Effect of One-Percentage Point Change in Assumed Health Care Cost Trend Rates [Abstract]      
Service and interest costs for 2014 0.2us-gaap_DefinedBenefitPlanEffectOfOnePercentagePointIncreaseOnServiceAndInterestCostComponents    
Service and interest costs for 2014 (0.1)us-gaap_DefinedBenefitPlanEffectOfOnePercentagePointDecreaseOnServiceAndInterestCostComponents1    
Postretirement benefit obligation at December 31, 2014 5.0us-gaap_DefinedBenefitPlanEffectOfOnePercentagePointIncreaseOnAccumulatedPostretirementBenefitObligation    
Postretirement benefit obligation at December 31, 2014 (4.5)us-gaap_DefinedBenefitPlanEffectOfOnePercentagePointDecreaseOnAccumulatedPostretirementBenefitObligation1    
Pension Plan [Member]      
Defined Benefit Plan, Weighted Average Assumptions Used in Calculating Net Periodic Benefit Cost [Abstract]      
Discount rate 4.20%us-gaap_DefinedBenefitPlanAssumptionsUsedCalculatingNetPeriodicBenefitCostDiscountRate
/ us-gaap_DefinedBenefitPlansDisclosuresDefinedBenefitPlansAxis
= us-gaap_PensionPlansDefinedBenefitMember
[1] 3.30%us-gaap_DefinedBenefitPlanAssumptionsUsedCalculatingNetPeriodicBenefitCostDiscountRate
/ us-gaap_DefinedBenefitPlansDisclosuresDefinedBenefitPlansAxis
= us-gaap_PensionPlansDefinedBenefitMember
3.90%us-gaap_DefinedBenefitPlanAssumptionsUsedCalculatingNetPeriodicBenefitCostDiscountRate
/ us-gaap_DefinedBenefitPlansDisclosuresDefinedBenefitPlansAxis
= us-gaap_PensionPlansDefinedBenefitMember
Expected long-term rate of return 7.75%us-gaap_DefinedBenefitPlanAssumptionsUsedCalculatingNetPeriodicBenefitCostExpectedLongTermReturnOnAssets
/ us-gaap_DefinedBenefitPlansDisclosuresDefinedBenefitPlansAxis
= us-gaap_PensionPlansDefinedBenefitMember
7.75%us-gaap_DefinedBenefitPlanAssumptionsUsedCalculatingNetPeriodicBenefitCostExpectedLongTermReturnOnAssets
/ us-gaap_DefinedBenefitPlansDisclosuresDefinedBenefitPlansAxis
= us-gaap_PensionPlansDefinedBenefitMember
7.75%us-gaap_DefinedBenefitPlanAssumptionsUsedCalculatingNetPeriodicBenefitCostExpectedLongTermReturnOnAssets
/ us-gaap_DefinedBenefitPlansDisclosuresDefinedBenefitPlansAxis
= us-gaap_PensionPlansDefinedBenefitMember
Future compensation growth rate 0.00%us-gaap_DefinedBenefitPlanAssumptionsUsedCalculatingNetPeriodicBenefitCostRateOfCompensationIncrease
/ us-gaap_DefinedBenefitPlansDisclosuresDefinedBenefitPlansAxis
= us-gaap_PensionPlansDefinedBenefitMember
3.00%us-gaap_DefinedBenefitPlanAssumptionsUsedCalculatingNetPeriodicBenefitCostRateOfCompensationIncrease
/ us-gaap_DefinedBenefitPlansDisclosuresDefinedBenefitPlansAxis
= us-gaap_PensionPlansDefinedBenefitMember
3.00%us-gaap_DefinedBenefitPlanAssumptionsUsedCalculatingNetPeriodicBenefitCostRateOfCompensationIncrease
/ us-gaap_DefinedBenefitPlansDisclosuresDefinedBenefitPlansAxis
= us-gaap_PensionPlansDefinedBenefitMember
Other Postretirement Benefit Plan [Member]      
Defined Benefit Plan, Weighted Average Assumptions Used in Calculating Net Periodic Benefit Cost [Abstract]      
Discount rate 4.10%us-gaap_DefinedBenefitPlanAssumptionsUsedCalculatingNetPeriodicBenefitCostDiscountRate
/ us-gaap_DefinedBenefitPlansDisclosuresDefinedBenefitPlansAxis
= us-gaap_OtherPostretirementBenefitPlansDefinedBenefitMember
[2] 3.40%us-gaap_DefinedBenefitPlanAssumptionsUsedCalculatingNetPeriodicBenefitCostDiscountRate
/ us-gaap_DefinedBenefitPlansDisclosuresDefinedBenefitPlansAxis
= us-gaap_OtherPostretirementBenefitPlansDefinedBenefitMember
3.60%us-gaap_DefinedBenefitPlanAssumptionsUsedCalculatingNetPeriodicBenefitCostDiscountRate
/ us-gaap_DefinedBenefitPlansDisclosuresDefinedBenefitPlansAxis
= us-gaap_OtherPostretirementBenefitPlansDefinedBenefitMember
Expected long-term rate of return 0.00%us-gaap_DefinedBenefitPlanAssumptionsUsedCalculatingNetPeriodicBenefitCostExpectedLongTermReturnOnAssets
/ us-gaap_DefinedBenefitPlansDisclosuresDefinedBenefitPlansAxis
= us-gaap_OtherPostretirementBenefitPlansDefinedBenefitMember
0.00%us-gaap_DefinedBenefitPlanAssumptionsUsedCalculatingNetPeriodicBenefitCostExpectedLongTermReturnOnAssets
/ us-gaap_DefinedBenefitPlansDisclosuresDefinedBenefitPlansAxis
= us-gaap_OtherPostretirementBenefitPlansDefinedBenefitMember
0.00%us-gaap_DefinedBenefitPlanAssumptionsUsedCalculatingNetPeriodicBenefitCostExpectedLongTermReturnOnAssets
/ us-gaap_DefinedBenefitPlansDisclosuresDefinedBenefitPlansAxis
= us-gaap_OtherPostretirementBenefitPlansDefinedBenefitMember
Future compensation growth rate 0.00%us-gaap_DefinedBenefitPlanAssumptionsUsedCalculatingNetPeriodicBenefitCostRateOfCompensationIncrease
/ us-gaap_DefinedBenefitPlansDisclosuresDefinedBenefitPlansAxis
= us-gaap_OtherPostretirementBenefitPlansDefinedBenefitMember
0.00%us-gaap_DefinedBenefitPlanAssumptionsUsedCalculatingNetPeriodicBenefitCostRateOfCompensationIncrease
/ us-gaap_DefinedBenefitPlansDisclosuresDefinedBenefitPlansAxis
= us-gaap_OtherPostretirementBenefitPlansDefinedBenefitMember
0.00%us-gaap_DefinedBenefitPlanAssumptionsUsedCalculatingNetPeriodicBenefitCostRateOfCompensationIncrease
/ us-gaap_DefinedBenefitPlansDisclosuresDefinedBenefitPlansAxis
= us-gaap_OtherPostretirementBenefitPlansDefinedBenefitMember
Discount rate before remeasurement of pension or postretirement liability [Member] | Other Postretirement Benefit Plan [Member]      
Defined Benefit Plan, Weighted Average Assumptions Used in Calculating Net Periodic Benefit Cost [Abstract]      
Discount rate   3.10%us-gaap_DefinedBenefitPlanAssumptionsUsedCalculatingNetPeriodicBenefitCostDiscountRate
/ us-gaap_DefinedBenefitPlansDisclosuresDefinedBenefitPlansAxis
= us-gaap_OtherPostretirementBenefitPlansDefinedBenefitMember
/ cbb_DiscountRateusedformeasuringNetPeriodicBenefitCostAxis
= cbb_DiscountratebeforeremeasurementofpensionorpostretirementliabilityMember
[2]  
Discount rate after remeasurement of pension or postretirement liability [Member] | Other Postretirement Benefit Plan [Member]      
Defined Benefit Plan, Weighted Average Assumptions Used in Calculating Net Periodic Benefit Cost [Abstract]      
Discount rate   3.90%us-gaap_DefinedBenefitPlanAssumptionsUsedCalculatingNetPeriodicBenefitCostDiscountRate
/ us-gaap_DefinedBenefitPlansDisclosuresDefinedBenefitPlansAxis
= us-gaap_OtherPostretirementBenefitPlansDefinedBenefitMember
/ cbb_DiscountRateusedformeasuringNetPeriodicBenefitCostAxis
= cbb_DiscountrateafterremeasurementofpensionorpostretirementliabilityMember
[2]  
[1] Discount rate used for the remeasurement of the management pension plan in May 2013 was consistent with the discount rate previously established.
[2] For the period January 1, 2013 through July 31, 2013, the date of the remeasurement, we used a 3.10% discount rate. From that date through December 31, 2013, we used a 3.90% discount rate.