We present a general heuristicfor the median problem for induced breakpoints on genomes with unequal gene content and incorporate this into a routine for estimating optimal gene orders for the ancestral genomes in a fixed phylogeny. The routine is applied to a phylogenetic study of an up-to-date set of completely sequenced protistmitochondrialgenomes, confirming some ofthe recent sequence-based groupings which have been proposed and, conversely, confirming the usefulness of the breakpoint method as a phylogenetic tool even for small genomes.