This note summarizes the economic case for completing the European Banking Union with a European Deposit Insurance Scheme (EDIS). The note highlights the role of the EDIS against panic-driven bank runs that might trigger sovereign crises in a doom loop, and spread across the Banking Union via several channels of financial contagion. The main takeaways that we can draw are three. First, the EDIS can be successful only if it acts fast and its commitment to intervene is perceived as credible. Second, there seems to be little evidence that the EDIS could generate an unwarranted cross-subsidization from the less vulnerable to the more vulnerable countries of the Banking Union. Third, there exist several mechanisms to correct bank incentives against the effects of legacy risk and moral hazard that the EDIS might bring about, and some of them are already into place.