What do the Lockerbie and US-Shrimps cases, the Swordfish dispute and the Southern Bluefin Tuna arbitration have in common? Often cited when addressing norm conflicts in international law, they were instrumental in moving interface conflicts center-stage, raising more general questions about unity and pluralism in international law. But a common terminology focused solely on conflict of norms does not account for the institutional setting in which conflict management takes place. This contribution focuses on global courts, arguing that in order to assess their institutional dimension, a better understanding of their respective judicial hermeneutics is needed. Through comparing landmark cases from three different international jurisdictions, and contrasting them with cases that could have, but did not, raise questions of conflicting regimes, I develop a framework to further investigate the conditions under which courts address conflicts and the legal tools they use to solve them.