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We consider the problem of sorting an arbitrary permutation of length n using substring reversals of length 2 or 3. This has been called "short swaps ". We give an upper bound of (5/24) n2 + O(nlogn), improving the previous ( 1/4 ) n2 upper bound. We also show that there is a short swap sorting network with ( 1/4 ) n2 +O(nlogn) comparators and depth n.