Mass domestic opposition increasingly challenges actors and institutions of the European Union. While scholars have analyzed the consequences of public contestation on cooperation among member states, less attention has been paid to its effects on cooperation with non-EU members. Yet, after the UK’s withdrawal, the risk of encouraging further exits has reduced the scope of differentiated integration for countries outside the EU. How do these changes in the bargaining space affect public support for international cooperation in non-EU countries? To answer this question, we exploit that voters in Switzerland have been faced with two EU-related policy proposals, one of which would considerably deepen relations with the EU, whereas the other would significantly lower levels of Swiss-EU cooperation. Drawing on a panel survey fielded between November 2019 and February 2021 and an embedded survey experiment, this paper shows how the ups and downs of the Brexit process altered the expected consequences of non-cooperative referendum outcomes, and in turn Swiss vote intentions in EU referendums. Our findings show how the withdrawal of individual countries from international organizations change public expectations about the costs of non-cooperation, and highlight the influence of the geopolitical context on support for international cooperation.