Evolution operates on whole genomes through mutations that change the order and strandedness of genes within the genomes. Thus analyses of gene-order data present new opportunities for discoveries about deep evolutionary events, provided that sufficiently accurate methods can be developed to reconstruct evolutionary trees. In this paper we present two new methods of character coding for parsimony-based analysis of genomic rearrangements: one called MPBE-2, and a new parsimony-based method which we call MPME (based on an encoding of Bryant), both variants of the MPBE method. We then conduct computer simulations to compare this class of methods to distance-based methods (NJ under various distance measures). Our empirical results show that two of our new methods return highly accurate estimates of the true tree, outperforming the other methods significantly, especially when close to saturation.