As the global banking crisis intensified in the fall of 2008, governments announced comprehensive rescue packages for financial institutions. In this paper, we put the joint response of euro area bank and sovereign CDS premia under the microscope. We find that the bank rescue packages led to a clear structural break in these premia's comovement, which had been rather tight and stable in the weeks preceding the intensification of the crisis. Firstly, the packages induced a decrease in risk spreads for banks at the expense of a marked increase in risk spreads for governments. Secondly, we show that in addition to this one-off jump in the levels of CDS spreads, the packages strongly increased the sensitivity of sovereign risk spreads to any further aggravation of the crisis. At the same time, the sensitivity of bank credit risk premia declined and became more sovereign-like, reflecting the extensive government guarantees of banking sector liabilities.