Throughout the last two decades international negotiations have been predominantly analysed from the perspective of rationalist bargaining theory. But most recently, constructivists have pointed to a different mechanism that may facilitate agreement among multiple parties: processes of argumentation. Indeed, numerous empirical studies were successful in showing that words have the power to change the initial bargaining position of an actor and thereby impact on the outcome of multilateral negotiations. Rationalists have so far been unable to capture this important role of argumentative talk within their conceptual framework. Therefore, this article introduces a theory of rational persuasion, which I call functional persuasion theory. According to this theory argument-based changes in bargaining positions are entirely belief-driven and are not due to a reformulation of agents’ preferences, as constructivists hold. The explanatory power of functional persuasion theory is demonstrated in the empirical part of this article by testing it against the most prominent constructivist explanations of argumentative persuasion.