This study proposes a principled approach to discretion in international adjudication. The main thesis defended is that international adjudicative discretion is not unfettered of legal considerations, but instead bound by abstract legal norms, particularly by general principles of law and principles inherent to the concept of law. These legal norms guide international adjudicators while deciding issues seemly unregulated by specific legal norms. We will demonstrate that other approaches, either openly arguing for an unfettered discretion, or implying such, are unsound both from a conceptual as from a practical point of view. In order to demonstrate our position, we test our more abstract points against the background of the practice of international courts and tribunals, with a particular emphasis in the International Court of Justice and investment treaty tribunals. We do so in the belief that the different settings in which disputes are adjudicated do not mandate a different approach to adjudicative discretion, which instead derives from main function of these different tribunals, the adjudication of a dispute in accordance with law. We revisit for these purposes some of the most salient contexts in which adjudicators are faced with first impression cases, dealing both with procedural and substantial issues.