Given a set of d dimensional objects, a skyline query finds the objects ("skyline") that are not dominated by others. However, skylines do not always provide useful query results to users, and existing methods of various skyline queries have at least one of the following drawbacks: (1) the size of skyline objects can not be controlled, or can be only increased or only decreased but not both; (2) skyline objects do not have built-in ranks; (3) skylines do not reflect users' weights (preferences) at different dimensions. In this paper, we propose a unified approach, the -skyline, to effectively solve all three drawbacks. We explore the properties of -skylines and propose several different algorithms to compute -skylines.