The convergence and subsequent divergence of sovereign spreads in the Euro Area after 2000 and after 2008, respectively, is a puzzle that has mainly been explained so far by a surge in risk aversion after 2008 or as evidence of multiple equilibria. We propose another explanation, based on the availability of bailouts by Euro Area institutions, that was first perceived as an implicit guarantee on the sovereign debt of Euro countries and was then formalized with the establishment of institutions such as the EFSF and the ESM. The limited lending capacity of these institutions is a channel of contagion between the spreads of different countries, as one country needing (or being perceived as close to needing) a bailout diminishes the prospects of another country receiving a bailout as well. We propose a model in this direction and explore some implications of such bailout mechanisms.