Extensive research expects systematic differences in the design of international organizations (IOs) based on the regime composition of their memberships. Yet so far, empirical analyses have found limited support for this expectation. This article resolves this puzzle by providing a new understanding of how the regime composition of IOs shapes their institutional design. Theoretically, it argues that this relationship is moderated by a critical but overlooked factor: the governance purpose of IOs, as expressed in the distinction between general-purpose and task-specific organizations. Empirically, it provides a comprehensive analysis of how changes in regime composition have affected institutional design in 40 IOs from 1950-2019. The findings show that the regime composition of IOs indeed is related to their institutional design, but only in general-purpose organizations, which present democracies and autocracies with more divergent design incentives than task-specific organizations. The article suggests that democracy, autocracy, and international cooperation are linked in more complex and contingent ways than understood in previous research.