Abstract Computational models of argument could play a valuable role in persuasion technologies for behaviour change (e.g. persuading a user to eat a more healthy diet, or to drink less, or to take more exercise, or to study more conscientiously, etc). For this, the system (the persuader) could present arguments to convince the user (the persuadee). In this paper, we consider asymmetric dialogues where only the system presents arguments, and the system maintains a model of the user to determine the best choice of arguments to present (including counterarguments to key arguments believed to be held by the user). The focus of the paper is on the user model, including how we update it as the dialogue progresses, and how we use it to make optimal choices for dialogue moves.