This paper outlines a model of argumentation that formulates the processes by which international and comparative human rights law influence the reasoning of domestic judges. I argue that the persuasive influence of such law flows from, and is justifiable by reference to, a distinctive mode of rational argumentation centred around precedent and analogy. If sound, this model helps explain how persuasive influence may be distinguished from political or ideological power (i.e. authority) and how decisions to use such law are constrained by formal and informal institutions of interpretation i.e. are justifiable in jurisprudential terms.