The stability of a banking system ultimately depends on the strength and credibility of the fiscal backstop. While large countries can still afford to resolve large global banks on their own, small and medium-sized countries face a policy choice. This paper investigates the impact of resolution on banking structure. The financial trilemma model suggests that smaller countries can either conduct joint supervision and resolution of their global banks (based on single point of entry resolution) or reduce the size of their global banks and move to separate resolution of these banks' national subsidiaries (based on multiple point of entry resolution). Euro-area countries are heading for joint resolution based on burden sharing, while the United Kingdom and Switzerland have implemented policies to downsize their banks.