International tribunals confront a “Judicial Trilemma.” More specifically the states that design, and the judges that serve on, international courts face an interlocking series of tradeoffs among three core values: (1) judicial independence, the freedom of judges to decide cases on the facts and the law; (2) judicial accountability, structural checks on judicial authority found most prominently in international courts in reappointment and reelection processes; and (3) judicial transparency, mechanisms that permit the identification of individual judicial positions (such as through individual opinions and dissents). The Trilemma is that it is possible to maximize, at most, two of these three values. Drawing on interviews with current and former judges at leading international courts, this article unpacks the logic underlying the Judicial Trilemma, and traces the varied ways in which this logic manifests itself in the design and operation of the International Court of Justice, European Court of Human Rights, Court of Justice of the European Union, and the World Trade Organization's Appellate Body. The Judicial Trilemma does not identify an “ideal” court design. Rather it provides a framework that enables international actors to understand the inevitable tradeoffs that international courts confront, and thereby helps to ensure that these tradeoffs are made deliberately and with a richer appreciation of their implications.