Why do reputations matter in international relations? This study tackles a core debate by proposing the concept of influence-specific reputations (ISR). We theorize that reputation adherence depends on an actor's influence. Using two survey experiments—one abstract and one detailed U.S.-Iran case—we demonstrate large country-specific reputations coexist with moderately sized leader-specific ones. According to our ISR theory, leaders' reputations are most impactful when they're highly influential in decision-making.