In this paper, we present a new approach for quickly computing the histograms of a set of unrotating rectangular regions. Although it is related to the well-known Integral Histogram (IH), our approach significantly outperforms it, both in terms of memory requirements and of response times. By preprocessing the region of interest (ROI) computing and storing a temporary histogram for each of its pixels, IH is effective only when a large amount of histograms located in a small ROI need be computed by the user. Unlike IH, our approach, called Min-Space Integral Histogram, only computes and stores those temporary histograms that are strictly necessary (less than 4 times the number of regions). Comparative tests highlight its efficiency, which can be up to 75 times faster than IH. In particular, we show that our approach is much less sensitive than IH to histogram quantization and to the size of the ROI.