The R*-tree is a state-of-the-art spatial index structure. It has already found its way into commercial systems. The most important improvement of the R*-tree over the original R-tree is that it utilizes forced reinsertion. That is, if a disk page overflows, some objects are removed from the page and reinserted into the index. The goals are: (a) to reduce the MBR area; and (b) to keep the shape of the MBR close to a square. However, no existing work consists of a unified metric which can be used to balance the two criteria. For example, if there are two methods to remove objects from a rectangle, and one results in a rectangle with smaller area, while the other results in a square with slightly larger area, which method shall we choose? The R*-tree algorithm selects objects whose distances to the center of the page's MBR are the largest. However, this is not optimal. In this paper, we formally define the quality of a rectangle and the gain to shrink a rectangle. Then we provide a...