This paper delves into Hungarian public attitudes toward the EU, and public perceptions of EU policies in Hungary. The analysis digs deeper than the standard “remain or leave” question concerning the EU, trying to get a more nuanced picture of how Hungarians perceive the policy balance of EU membership and their country’s place within the EU, two decades after EU accession. We present what the EU means to Hungarians, what they consider to be the main advantages and disadvantages of EU membership, and how they assess the economic balance of EU membership. This paper focuses especially on the question of how much Europe Hungarians actually want: How strong is domestic support for deeper integration on the one hand, and how strong is the support for a policy of national sovereignty on the other? With these questions in mind, we examine the public policy areas in which Hungarians would like to see the EU as the competent decision-making level, and the issues that they would prefer to remain exclusively within national competence. Building on this, we use a typology based on support for EU membership and national/EU competences to classify domestic attitudes towards the role of the EU. By examining the interplay between public opinion and policy decisions, this paper offers valuable insights into the broader implications of Euroscepticism in Hungary.