Bank resolution is key to avoiding a repetition of the global financial crisis, where failing financial institutions had to be bailed out with taxpayers’ money. It permits recapitalizing banks or alternatively winding them down in an orderly fashion without creating systemic risk. Resolution measures, however, suffer from structural weakness. They are taken by States with territorially limited powers, yet they concern entities or groups with global activities and assets in many countries. Under traditional rules of private international law, these activities and assets are governed by the law of other States, which is beyond the remit of the State undertaking the resolution. This paper illustrates the conflict between resolution and private international law by taking the example of the European Union, where the limitations of cross-border issues are most acute. It explains the techniques and mechanisms provided in the Bank Resolution and Recovery Directive (BRRD) and the Single Resolution Mechanism (SRM) Regulation to make resolution measures effective in intra-Eurozone cases, in intra-EU conflicts with non-Euro Member States and in relation to third States. However, it also shows divergences in the BRRD's transposition into national law and flaws that have been uncovered through first cases decided by national courts. A brief overview of third country regimes furthermore highlights the problems in obtaining recognition of EU resolution measures abroad. This article argues that regulatory cooperation alone is insufficient to overcome these shortcomings. It stresses that the effectiveness of resolution will ultimately depend on the courts. Therefore, mere soft law principles of regulatory cooperation are insufficient. A more stable and uniform text on resolution is required, which could take the form of a legislative guide or, ideally, of a model law. It is submitted that such a text could pave the way for greater effectiveness of cross-border resolution.