This study provides a dynamic analysis of the lead-lag relationship between sovereign Credit Default Swap (CDS) and bond spreads of the highly indebted southern European countries, considering an extensive time sample from the period before the global financial crisis to the latest developments of the sovereign indebtedness in the euro area. We employ an integrated price discovery methodology on a rolling sample, with the intention of investigating the efficient pricing of credit risk in the CDS and bond markets and the possibility of CDS spreads causing rises in bond spreads. In addition, we attempt to depict the evolution of the price discovery process regarding the direction of influence from one market to the other. The rolling window analysis verifies that the price discovery process evolves over time, presenting frequent alternations concerning the leading market. We find that during periods of economic turbulence the CDS market leads the bond market in price discovery, incorporating the new information about sovereign credit risk faster and more efficiently than the bond market does. This regularity should be seriously considered by private and public participants as they make investment and funding decisions. Therefore, the motivation of our paper is to identify the dominant market in terms of price discovery during a period of economic turmoil and, thus, to provide insights for decision making to investment bodies and central governments.