A new method for computing evolutionary distances between DNA sequences is proposed. Contrasting with classical methods, the underlying model does not assume that sequence base compositions (A, C, G, and T contents) are at equilibrium, thus allowing unequal base compositions among compared sequences. This makes the method more efficient than the usual ones in recovering phylogenetic trees from sequence data when base composition is heterogeneous within the data set, as we show by using both simulated and empirical data. When applied to small-subunit ribosomal RNA sequences from several prokaryotic or eukaryotic organisms, this method provides evidence for an early divergence of the microsporidian Vairimorpha necatrix in the eukaryotic lineage.