Gu et al. gave a 2-approximation for computing the minimal number of inversions and transpositions needed to sort a permutation. There is evidence that, from the point of view of computational molecular biology, a more adequate objective function is obtained, if transpositions are given double weight. We present a (1+eps)-approximation for this problem, based on the exact algorithm of Hannenhalli and Pevzner, for sorting by reversals only.