Today, result sets of skyline queries are unmanageable due to their exponential growth with the number of query predicates. In this paper we discuss the incremental re-computation of skylines based on additional information elicited from the user. Extending the traditional case of totally ordered domains, we consider preferences in their most general form as strict partial orders of attribute values. After getting an initial skyline set our basic approach aims at interactively increasing the system's information about the user's wishes explicitly including indifferences. The additional knowledge then is incorporated into the preference information and constantly reduces skyline sizes. In fact, our approach even allows users to specify trade-offs between different query predicates, thus effectively decreasing the query dimensionality. We give theoretical proof for the soundness and consistence of the extended preference information and an extensive experimental evaluation of the efficiency of our approach. On average, skyline sizes can be considerably decreased in each elicitation step.