Over the last couple of years, there has been considerable debate on the need to “complete” the banking union. In this debate there has been little attention, however, to the omission of shadow banks from the supervision mandate given to the European Central Bank in and through the Single Supervisory Mechanism (SSM). The European Systemic Risk Board’s (ESRB) – confined to monitoring, as opposed to supervising – recently documented that Europe’s banking and non-banking financial institutions are as interconnected as ever. There cannot be any such thing as a completion of Europe’s banking union, we argue, without the establishment of formal European supervision of all non-banking institutions. We identify four potential, explanatory factors for the omission of shadow banking from the SSM mandate. This examination of factors that may help explain the SSM’s narrow supervision mandate, allows us to reflect on strategies – discursive as well as organizational – towards establishing pan-European supervision of all non-banking financial institutions.