Investor-state dispute settlement (ISDS) plays an increasingly important role in international trade resolution. The decisions have significant financial and in many cases policy implications, yet little is known about the formation of the ad-hoc panels and the decision-making process. Drawing on empirical evidence from interviews with key actors in the ISDS system, this article argues that influence plays a central role in both processes. The analysis further develops the framework for understanding influence in international decision-making to accommodate external factors (those visible to those appointing the decision-makers) and internal factors (those factors that become visible in the decision-making room). It draws our attention to the nuanced relationship and distinction between the characterization of influence in both contexts and poses a challenge to the traditional focus of appointments based on power and prestige which neglects the group decision-making context and the multifaceted construction of influence in this increasingly important method of adjudication.