: Skyline queries have recently received a lot of attention due to their intuitive query formulation: users can state preferences with respect to several attributes. Unlike numerical preferences, preferences over discrete value domains do not show an inherent total order, but have to rely on partial orders as stated by the user. In such orders typically many object values are incomparable, increasing the size of skyline sets significantly, and making their computation expensive. In this paper we explore how to enable interactive tasks like query refinement or relevance feedback by providing ‘prime cuts’. Prime cuts are interesting subsets of the full Pareto skyline, which give users a good overview over the skyline. They have to be small, efficient to compute, suitable for higher numbers of query predicates, and representative. The key to improved performance and reduced result set sizes is the relaxation of Pareto semantics to the concept of weak Pareto dominance. We argue that th...