The eurozone is caught in a ‘diabolical loop’ in which weak domestic banking systems damage sovereign fiscal positions and conversely, in which risky sovereign positions disproportionately threaten domestic banking stability. A European-level banking system could go a long way towards breaking this unfortunate loop and stabilising the eurozone. This would require a European safety net for cross-border banks. This paper sketches the building blocks of a European Deposit Insurance Fund. We calculate that such a Fund would amount to €55 billion for the 35 largest European banks. This Fund could be created over ten years through risk-based deposit insurance premiums levied on the top 35 banks. Once fully up and running, the Fund could also deal with the resolution of one or more of these 35 banks. The Fund would then be turned into a European Deposit Insurance and Resolution Fund. The paper aims to promote debate among policy-makers, industry and academia.