The aim of this paper is to explore the nature of conversational involvement as the result of specific discourse strategies deployed by the speaker (s) with the purpose of creating not only a coherent but above all a sufficiently unique representation of reality to promote the active participation of the interlocutor(s) in the task of sense-making. Through the analysis of one conversational story, recounted in a particular social setting, it is suggested, first of all, that rather than making a point or transmitting a specific message, the function of conversational stories may be that of resolving an interpersonal problem. The analysis also shows how the narrator "works" towards forcing the participation of the addressee(s), sometimes indirectly, through facilitating their reconstruction of the world of the story by introducing details, imagery and external evaluations, and sometimes directly, by means of discourse markers of interactivity. 1. Introduction