The enormous number of questions needed to acquire a full preference model when the size of the outcome space is large forces us to work with partial models that approximate the user's preferences. In this way we must devise elicitation strategies that focus on the most important questions and at the same time do not need to enumerate the outcome space. In this paper we focus on adaptive elicitation of GAI-decomposable preferences for top-k recommendation tasks in large combinatorial domains. We propose a method that interleaves the generation of top-k solutions with a heuristic selection of questions for refining the user preference model. Empirical results for a large combinatorial problem are given.