Preference-based queries (or skylines) play an im-portant role in cooperative query processing. However, their prohibitive result sizes pose a severe challenge to the paradigm?s practical applicability. Since skyline sizes can only be predicted under strong assumptions, we present a sophisticated user inter-face to interactively refine queries in case the respective skyline set proves to be too large. Our approach allows users to incre-mentally augment preferences given by their Hasse diagrams. Moreover, we prove the correctness of the incremented skyline and in our experiments show the approach's superior efficiency