Feng and Zhu defined the permutation tree structure to achieve a running time of O(nlogn) for Hartman and Shamir’s 1.5-approximation algorithm for sorting genomes by transpositions. The present work describes the first available implementation of this algorithm using permutation trees. Our analysis of Hartman and Shamir’s algorithm also leads to a modified 1.5-approximation algorithm that achieves in most cases a shorter sequence of transpositions that sorts a given permutation. Although our modified algorithm has a worst-case running time of O(n ²logn), in our experiments using real genomic data the running time is still very small.