When issuing user-specific queries, users often have a vaguely defined information need. Skyline queries identify the most “interesting” objects for users’ incomplete preferences, which provides users with intuitive query formulation mechanism. However, the applicability of this intuitive query paradigm suffers from a severe drawback. Incomplete preferences on domain values can often lead to impractical skyline result sizes. In particular, this challenge is more critical over categorical domains. This paper addresses this challenge by developing an iterative elicitation framework. While user preferences are collected at each iteration, the framework aims to both minimize user interaction and maximize skyline reduction. The framework allows to identify a reasonably small and focused skyline set, while keeping the query formulation still intuitive for users. All that is needed is answering a few well-chosen questions. We perform extensive experiments to validate the benefits of our strategy and prove that a few questions are enough to acquire a desired manageable skyline set.