This paper addresses the following questions. Is there evidence of financial contagion in the Eurozone? To what extent a country's vulnerability to contagion depends on "fundamentals" as opposed the government's "credibility"? We look at the empirical evidence on European sovereigns CDS spreads and estimate an econometric model where a crucial role is played by time varying parameters. We model CDS spread changes at country level as reflecting three different factors: a Global sovereign risk factor, a European sovereign risk factor and a Financial intermediaries risk factor. Our main findings are as follows. First, Unlike the US subprime crisis which affected all European sovereign risks, the Greek crisis is largely a matter concerning the Euro Zone. Second, differences in vulnerability to contagion within the Eurozone are even more remarkable: the core Eurozone members become less vulnerable to EUZ contagion, possibly due to a safe-heaven effect, while peripheric countries become more vulnerable. Finally, market fundamentals go a long way in explaining these differences: they jointly explain between 54 and 80% of the cross-country variation in idiosyncratic risks and in the vulnerability to contagion, largely supporting the "wake-up call" hypothesis according to which market participants become more wary of market fundamentals during financial crises.