Minority governments are anything but rare phenomena: more than one third of democratic governments do not rely on a secured majority in parliament. Previous research has extensively examined the formation of minority governments, and political scientists have long debated their performance indicating that minority governments may perform quite as well, sometimes even better, than majority governments. However, beyond these scholarly debates, we do not know much about what citizens think about minority governments. How do citizens evaluate minority and majority governments? Under which conditions do citizens prefer the formation of minority governments? We argue that citizens’ evaluations are influenced by cues from public opinion, their strategic self-interest and their political flexibility. Accordingly, citizens are more likely to support their formation when public support for minority governments is high and when it secures greater policy influence of one’s preferred party. Moreover, the less a citizen is attached to a specific party or party bloc, the more she prefers minority governments. These hypotheses are tested based on a two-round conjoint survey experiment in Germany we conducted in the run-up to the general election in 2021 (N = 2.750). Germany is a particular interesting case, since two-party majority coalitions were long time the norm. Increasing political fragmentation, however, now requires alternative forms of majority formation. Minority governments and flexible majorities, hence, attract increasing public attention. The findings of this study have important implications for our understanding of different types of government and their perceived political legitimacy, especially in political contexts facing party fragmentation.