The goal of expanding participation in the European Banking Union was to allow the “outs” to enter into close co-operation, but it did not explicitly include the simultaneous joining of the Exchange Rate Mechanism (ERM II). It now appears entry into ERM II requires entry into the Banking Union. Focusing on the cases of Bulgaria and Croatia, this article attempts to respond to various questions. What is the rationale behind the double requirement of having simultaneously to apply to become a member of ERM II and the Banking Union? What are the advantages of preparing to become a full member of the euro area and the SSM? It is evident from the research undertaken in this article that there are clear benefits of close co-operation for these Member States whose domestic currencies are already linked to the euro, in view of the dominant position eurozone banks have in their respective domestic markets.