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Spatial objects other than points and boxes can be stored in spatial indexes, but the techniques usually require the use of approximations that can be arbitrarily bad. This leads to poor performance and highly inaccurate responses to spatial queries. The situation can be improved by storing some objects in the index redundantly. Most spatial indexes permit no flexibility in adjusting the amount of redundancy. Spatial indexes based on z-order permit this flexibility. Accuracy of the query response increases with redundancy, (there is a “diminishing return” effect). Search time, as measured by disk accesses first decreases and then increases with redundancy. There is, therefore, an optimal amount of redundancy (for a given data set). The optimal use of redundancy for z-order is explored through analysis of the z-order search algorithm and through experiments.