In recent years, there has been greater scholarly enquiry into explaining variation in support for European Union membership. We theorise that one cause of such variation is likely to be non-political psychological predispositions, such as one's personal values. We test this proposition by applying Schwartz's theory of basic human values to predict voting intentions in hypothetical referendums on EU membership. We theorise that these values determine both voting intentions and more proximate explanatory variables of support for EU membership: attitudes to immigration and identifying as European. Using data on 13 countries from the European Social Survey (N=24,703 citizens) and multigroup structural equation modeling, we demonstrate that this psychological framework effectively predicts voting intentions, notably in terms of the consistent cross-country evidence for indirect effects of values on support for membership via European identity and attitudes to immigration. We then discuss the implications of our findings, including differences in effects between countries.