I analyze the optimal design of banking supervision in the presence of cross-border lending. Cross-border lending could imply that an individual bank failure in one country could trigger negative spillover effects in another country. Such cross-border contagion effects could turn out to be important in the EU because national banking problems could easily spread via the highly integrated interbank market. I show that if benevolent supervisors are accountable only to their own jurisdiction, they will not take cross-border contagion effects into account. Supervisors with such a national mandate fail to implement the optimum from a supranational perspective. In consequence, the probability of a bank failure will be inefficiently high. Against the background of this result, I argue in favor of institutionalizing an EU Supervisory Coordination Authority to which national supervisors are accountable.