Evolution of mitochondrial genes is far from clock-like. The substitution rate varies considerably between species, and there are many species that have a significantly increased rate with respect to their close relatives. There is also considerable variation among species in the rate of gene order rearrangement. Using a set of 55 complete arthropod mitochondrial genomes, we estimate the evolutionary distance from the common ancestor to each species using protein sequences, tRNA sequences, and breakpoint distances (a measure of the degree of genome rearrangement). All these distance measures are correlated. We use relative rate tests to compare pairs of related species in several animal phyla. In the majority of cases, the species with the more highly rearranged genome also has a significantly higher rate of sequence evolution. Species with higher amino acid substitution rates in mitochondria also have more variable amino acid composition in response to mutation pressure. We discuss the possible causes of variation in rates of sequence evolution and gene rearrangement among species and the possible reasons for the observed correlation between the two rates.