How do voters want their governments to respond when another country unilaterally withdraws from an international institution? We distinguish between negotiation approaches that vary in the degree to which they accommodate the withdrawing state's demands and argue that negotiation preferences are shaped by two issues. The first is voters’ exposure to the costs and benefits of accommodation. This exposure varies across issues, and we argue that citizens will generally prefer non-accommodation on zero-sum issues, but support more accommodation on cooperation issues, where non-accommodation puts existing cooperation gains at risk. Second, withdrawal negotiations create precedents, and citizens should therefore be less willing to accommodate the more they are concerned about the ripple effects of accommodation on the institution's stability. These concerns also confront citizens with two types of dilemmas depending on how favorably they view the institution themselves. To test our argument, we use survey evidence and a conjoint experiment conducted in Germany and Spain during the Brexit negotiations. We find that respondents overall are more willing to accommodate the UK on cooperation issues than on zero-sum issues, but also find evidence that Euroskeptics and Europhiles confront different issue-specific dilemmas. Our paper contributes to a better understanding of the dynamics surrounding the challenges to multilateralism that have proliferated in recent years.