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The KLEE'S MESURE of n axis-parallel boxes in R^d is the volume of their union. It can be computed in time within O(n^d/2) in the worst case. We describe three techniques to boost its computation: one based on some type of "degeneracy" of the input, and two ones on the inherent "easiness" of the structure of the input. The first technique benefits from instances where the MAXIMA of the input is of small size h, and yields a solution running in time within O(n^2d-2h+ h^d/2) ⊆ O(n^d/2). ThearXiv:1505.02855v2 fatcat:lpg4qriqnrddpkb2dm7ocmsamm