This research note examines voter preferences in Swiss-EU relations. We identify large shares of cross-pressured voters, i.e., citizens who support the bilateral treaties but wish to either control immigration into Switzerland or oppose a liberalization of social protection measures on the job market. Voters experiencing a trade-off between immigration control and international cooperation are mainly located on the Right. Their share decreased between 2015 and 2019, whereas the share of neutral voters sharply increased. Moreover, negotiations about an Institutional Framework Agreement between Switzerland and the EU have given rise to a new trade-off – namely between social protection and international cooperation – with cross-pressured voters mainly concentrated on the Left. This tension has generated a high share of undecided voters. When pressured to decide on these trade-offs, cross-pressured and neutral voters opt for the bilateral treaties over immigration control, whereas they prefer social protection over the new agreement. Partisanship is a strong predictor of these choices.