Skypatterns are important since they enable to take into account user preference through Pareto-dominance. Given a set of measures, a skypattern query finds the patterns that are not dominated by others. In practice, different users may be interested in different measures, and issue queries on any subset of measures (a.k.a subspace). This issue was recently addressed by introducing the concept of skypattern cubes. However, such a structure presents high redundancy and is not well adapted for updating operations like adding or removing measures, due to the high costs of subspace computations in retrieving skypatterns. In this paper, we propose a new structure called Compressed Skypattern Cube (abbreviated CSKYC), which concisely represents a skypattern cube, and gives an efficient algorithm to compute it. We thoroughly explore its properties and provide an efficient query processing algorithm. Experimental results show that our proposal allows to construct and to query a CSKYC very efficiently.