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Given a set of multidimensional points, a skyline query returns the interesting points that are not dominated by other points. It has been observed that the actual cardinality (s) of a skyline query result may differ substantially from the desired result cardinality (k), which has prompted studies on how to reduce s for the case where k<;s. This paper goes further by addressing the general case where the relationship between k and s is not known beforehand. Due to their complexity, the existing pointwise ranking and set-wide maximization techniques are not well suited for this problem. Moreover, the former often incurs too many ties in its ranking, and the latter is inapplicable for k>;s. Based on these observations, the paper proposes a new approach, called skyline ordering, that forms a skyline-based partitioning of a given data set such that an order exists among the partitions. Then, set-wide maximization techniques may be applied within each partition. Efficient algorithms are developed for skyline ordering and for resolving size constraints using the skyline order. The results of extensive experiments show that skyline ordering yields a flexible framework for the efficient and scalable resolution of arbitrary size constraints on skyline queries.