This paper develops a framework for analyzing how international courts promote compliance with international law. It first develops a matrix of four approaches through which international courts promote compliance. Integrating theories of international relations and international law, the matrix has two fault lines based on the logic (rationalist logic of consequences or constructivist logic of appropriateness) and means (direct or indirect/mediated) of international courts’ impact. Based on the matrix’s “menu” of approaches available to international courts, the paper accounts for the variation in the approaches employed by courts in terms of four dimensions of their institutional design—precision, independence, access, and embeddedness—inspired by the international relations scholarship on legalization. “Precision” refers to how clearly a court’s institutional design and law are defined. “Independence” reflects its judicial discretion and impartiality. “Access” is determined by how many different types of actors can participate in the court. “Embeddedness” indicates the extent to which an international court is an integral part of a developed international legal regime. These variables’ impact on international court behavior is elucidated through a comparative analysis of all the twenty-five international courts in the international system, and case studies of the World Trade Organization’s Dispute Settlement Understanding, European Court of Justice, and International Criminal Court. This analysis supports several conjectures. For example, high access levels provide international courts the opportunity to adopt indirect approaches, and low embeddedness levels can draw courts towards the constructivist approaches. Thus, the framework serves to explain the significant variation in international courts fulfil their core mandate of promoting compliance and, furthermore, offers guidance for international courts aiming to maximize their impact in international politics.