Following the sovereign debt crisis of 2012, some southern European countries have debated proposals to leave the Euro. We evaluate this policy change in a standard monetary model with seigniorage financing of the deficit. The main novel feature is that we depart from rational expectations while maintaining full rationality of agents in a sense made very precise. Our first contribution is to show that small departures from rational expectations imply that inflation upon exit can be orders of magnitude higher than under rational expectations. Our second contribution is to provide a framework for policy analysis in models without rational expectations.