Nearly 30 years after Duverger introduced the model of a semi-presidential system of government, a plurality of the world?s democracies fit that type. Yet political science still knows relatively little about the actual performance of these regimes, and in particular how important a role the president plays, which was one of the key questions posed by Duverger. In this paper, we consider the impact of semi-presidential subtypes (premier-presidential and president-parliamentary) on patterns of selection and deselection of prime ministers. We show that these subtypes can be clearly differentiated according to their degree of presidentialization and that premier-presidential systems tend to empower presidents relative to parties, as intended by their original founders, but that they also moderate that power through the requirement that the president maintain a parliamentary majority or else face cohabitation an opposition-led cabinet.