We explore the interplay between sovereign and bank credit risk in a setting where Danish authorities first let two Danish banks default rather than bail them out and then left the country's largest bank, Danske Bank, to recapitalize privately. We find that the correlation between bank and sovereign credit default swap (CDS) rates changed with these events, indicating that the non-bailout decisions and recapitalization helped to curb the feedback loop between bank and sovereign risk. Following the non-bailout events, the sensitivity to external shocks declined both for Danske Bank and for Danish sovereign debt, as measured by their CDS connection with CDS rates on the European banking sector. After Danske Bank was recapitalized, its exposure to the European banking sector reappeared, while that did not happen for Danish sovereign debt. This decoupling between CDS rates on sovereign and private bank debt indicates that the non-bailout policies succeeded in breaking the vicious circle generated by the risks on the bank and sovereign debts. Our results are reinforced by the use of an indirect testing approach and by focusing on CDS-quantiles.