How does support for European integration relate to left-right political ideology? Studies of political parties and elites often find that the relationship resembles an inverted U-curve, with support highest at the center of the scale and falling both towards the extreme left and extreme right ends. The same ‘horseshoe’ pattern has been observed with respect to public opinion as well, but recent studies question its generalizability across countries, time periods and measures of support for European integration. This article reports the most comprehensive study to date of the relationships between support for European integration (operationalized in several different ways) with self-placement on the left-right ideological scale and policy preferences for redistribution, immigration and gay rights. Based on data from the European Social Survey and Eurobarometer, I chart the patterns of covariation for all countries in the European Union between 2004 and 2020. The analysis introduces the use of flexible non-parametric methods (generalized additive models) and more appropriate measures of dependence (the distance correlation coefficient) than the usually-employed Pearson’s correlation and regression coefficients. I find that the relationship between public support for European integration and left-right ideology is weak and extremely heterogeneous across countries. The exact form of the relationship depends on the operationalization of European integration support, the country and the time period, but it rarely resembles the classic inverted U-curve. In fact, EU support is typically highest at the moderate left rather than at the center. The relationship of support for European integration with immigration attitudes is much stronger, stable and almost linear; with support for gay rights is also linear but considerably weaker than with immigration; with support for redistribution there is practically no relationship at all. There is some evidence that the strength of the link with different policy preferences peaks when the salience of the policy issue is highest. But there is much remaining variation that calls for an explanation.