To tackle the EU's persistent "crisis of legitimacy", many institutional reform options are on the table: new participatory instruments, more effective policies, or a more differentiated European integration. But what kind of EU do the citizens want? In this paper, we analyze to what degree European citizens derive their legitimacy beliefs from different facets of the EU's institutional design. We argue, first, that EU citizens generally prefer a Union that is more participatory (input), more transparent (throughput), and delivers effective policies (output). Second, however, we believe that people's legitimacy beliefs also strongly depend on their previous dispositions towards the EU and European integration. While Eurosceptic citizens prefer a differentiated Union with strong intergovernmental elements and relative benefits for their own country, Europhiles demand a less differentiated EU with a more supranational character that works for all countries similarly well. We test these theoretical expectations by conducting original conjoint survey experiments in six EU member states (Denmark, Germany, France, Hungary, Poland, Spain) with 2,000 respondents in each country. The results carry important implicants for the future of European integration. They imply that relatively broad reform coalitions among citizens should be feasible for reforms that increase the EU's input, output, and throughput legitimacy. However, reforms that touch upon the existing power distribution between Brussels and the member states are likely to be highly contested.