Under what conditions can regional and international courts (ICs) make decisions against their governments' preferences? To answer this much debated question, we develop a new, majoritarian model of state‐IC relations. It posits that in cases where well‐established ICs' positions are congruent with policy‐specific public opinion in leading member states, ICs can rule against their governments' position. We apply our approach to a series of landmark decisions by the Court of Justice of the European Union (CJEU) regarding United Nations sanctions against terror suspects. We find that the CJEU was able to harness growing public support to strengthen terror suspects' rights, punish states for superficial compliance with its rulings and ultimately broaden the Court's judicial review powers. Our analysis suggests that ICs can be agents of legal change and advance human rights against governments' resistance, but this role is conditional on the presence of public support.