Tractability results are rare in the comparison of gene orders for more than two genomes. Here we present a linear-time algorithm for the small parsimony problem (inferring ancestral genomes given a phylogeny on an arbitrary number of genomes) in the case gene orders are permutations, that evolve by inversions not breaking common gene intervals, and these intervals are organised in a linear structure. We present two examples where this allows to reconstruct the ancestral gene orders in phylogenies of several γ-Proteobacteria species and Burkholderia strains, respectively.We prove in addition that the large parsimony problem (where the phylogeny is output) remains NP-complete.