At the crossroad of preference learning and multicriteria decision aiding, recent researchs on preference elicitation provide useful methods for recommendation systems. In this paper, we consider (partial) lexicographic preferences. In this way, we can consider dilemmas and we show that these situations have a minor impact in practical cases. Based on this observation, we propose an algorithm for active learning of preferences. This algorithm solve the dilemmas by suggesting concrete alternatives which must be ranked by the user.