Phylogenetic reconstruction from gene-order data has attracted attention from both biologists and computer scientists over the last few years. So far, our software suite GRAPPA is the most accurate approach, but it requires that all genomes have identical gene content, with each gene appearing exactly once in each genome. Some progress has been made in handling genomes with unequal gene content, both in terms of computing pairwise genomic distances and in terms of reconstruction. In this paper, we present a new approach for computing the median of three arbitrary genomes and apply it to the reconstruction of phylogenies from arbitrary gene-order data. We implemented these methods within GRAPPAand tested them on simulated datasets under various conditions as well as on a real dataset of chloroplast genomes; we report the results of our simulations and our analysis of the real dataset and compare them to reconstructions made by using neighbor-joining and using the original GRAPPA on the same genomes with equalized gene contents. Our new approach is remarkably accurate both in simulations and on the real dataset, in contrast to the distance-based approaches and to reconstructions using the original GRAPPAapplied to equalized gene contents.