Can international organizations (IOs) boost support for their authority? We consider the effectiveness of appeals to the principle of complementarity, which holds that IOs only act when domestic institutions fail. Supporters of IOs like the International Criminal Court (ICC) frequently use complementarity as an argument to rally support for international action and spur domestic action. We evaluate the effectiveness of complementarity arguments using the largest survey experiment on the ICC to date, with more than 10,000 participants in five countries whose cooperation could be pivotal for the Court: Georgia, Israel, the Philippines, South Africa, and the United States. We find only modest evidence that complementarity arguments improve public support for either ICC investigations or domestic investigations—effects that vary across countries. This suggests that a major argument thought to legitimate IOs may not persuade global publics. Instead, an IO’s negative judgment of domestic actions may be perceived as paternalistic or, in Global South contexts, neocolonial.