Why do elites in some authoritarian regimes but not others remove from power the leaders who harm their interests? We develop a formal theory explaining this. The theory shows how elites' ambition prevents them from controlling authoritarian leaders. Because ambitious elites are willing to stage coups to acquire power even when the leader is good, ambition renders elites' claims that the leader's actions harm them less credible, making the other elites less likely to support coups. We show that the impact of the proportion of competent politicians on personalist regimes is non-monotonic: personalist regimes are most likely to emerge not only when there are few competent politicians but also when there are lots of them. We also provide insight into which elites become coup-plotters. The theory explains the emergence of personalist regimes, the frequency of coups, and why some authoritarian countries enjoy a more competent leadership than others.