: Skyline Queries have recently received a lot of attention due to their intuitive query capabilities. Following the concept of Pareto optimality all `best' database objects are returned to the user. However, this often results in unmanageable large result set sizes hampering the success of this innovative paradigm. As an effective remedy for this problem, trade-offs provide a natural concept for dealing with incomparable choices. But such trade-offs are not reflected by the Pareto paradigm. Thus, incorporating them into the users' preference orders and adjusting skyline results accordingly needs special algorithms beyond traditional skylining. For the actual integration of trade-offs into skylines, the problem of ensuring the consistency of arbitrary trade-off sets poses a demanding challenge. Consistency is a crucial aspect when dealing with multi-dimensional trade-offs spanning over several attributes. If the consistency should be violated, cyclic preferences may occur in ...