Abstract. Given a set of geospatial objects, the Best Region Search problem finds the optimal placement of a fixed-size rectangle so that the value of a user-defined utility function over the enclosed objects is maximized. The existing algorithm for this problem computes only the top result. However, this is often quite restrictive in practice and falls short in providing sufficient insight about the dataset. In this paper, we introduce the k-BRS problem, and we present a method for efficiently and progressively computing the next best result for any number of results k requested by the user. We show that our approach can accommodate additional constraints. In particular, we consider the requirement of computing the next best rectangle that has no or little overlap with the already retrieved ones, which reduces the repetition and redundancy in the results presented to the user. Our experimental evaluation demonstrates that our algorithms are efficient and scalable to large real-world dataset.