The spatial scan statistic is widely used to search for clusters. This article shows that the usually applied elimination of secondary clusters as implemented in SatScan is sensitive to smooth changes in the shape of the clusters. We present an algorithm for generation of a set of confocal elliptic windows and propose a new way to present the information when a spatial point process is considered. This method gives smooth changes for smooth expansions of the set of clusters. A simulation study is used to show how the elliptic windows outperforms the usual circular windows. The proposed method for graphical representation of the information in a set of clusters contain more information than just presenting nonoverlapping clusters. We suggest that more than one graphical representation of a set of clusters should be used to easily extract more information and to avoid pitfalls of the selected method.