What explains support for European Integration? Why did people on the Left oppose, and Right support, European Integration in the 1980s, but this pattern reverse in the 2020s? In contrast to the common account of European Integration as a new ‘cleavage’ in European politics, on a par with class, religion, and geography, we argue that citizens evaluate European Integration by what it has on offer for them. If Europe offers them a policy-bundle in line with their own (left-right) preferences, they support it. If not, they are opposed. In turn, the EU adjusts its policy-bundle in response to what the EU expects the public demands. Although sometimes out of tune, support for European Integration is a dance between the public self-interested assessment of Europe’s policy supply and Europe’s responsiveness to the public’s policy demand. We test this theory using individual-level public opinion data from all EU member states since the mid 1970s and a novel method for measuring the left-right policy location of EU legislative outputs over time.