The trade‐off between international cooperation gains and national sovereignty has become increasingly salient in recent years. This paper examines how voters assess this trade‐off in Switzerland, focusing on the choice between the economic benefits of EU integration versus sovereign immigration control. Using survey data, we identify voters for whom this choice is not clear, either because they are cross‐pressured (favouring Swiss‐EU bilateral treaties, while opposing increased immigration) or because they do not have clear preferences. We show that these are sizeable groups within the Swiss electorate and that in particular the potentially cross‐pressured mainly consist of politically mobilized, high‐income voters, supportive of right‐wing parties. Among the potentially cross‐pressured and voters with indistinct preferences, leaning towards the SVP strongly predicts a preference for immigration control over sustaining cooperation with the EU. Beyond this, our findings suggest that political variables have stronger explanatory power than individual‐level economic vulnerabilities in predicting choice.