We present a likelihood method for estimating codon usage bias parameters along the lineages of a phylogeny. The method is an extension of the classical codon-based models used for estimating dN/dS ratios along the lineages of a phylogeny. However, we add one extra parameter for each lineage: the selection coefficient for optimal codon usage (S), allowing joint maximum likelihood estimation of S and the dN/dS ratio. We apply the method to previously published data from Drosophila melanogaster, Drosophila simulans, and Drosophila yakuba and show, in accordance with previous results, that the D. melanogaster lineage has experienced a reduction in the selection for optimal codon usage. However, the D. melanogaster lineage has also experienced a change in the biological mutation rates relative to D. simulans, in particular, a relative reduction in the mutation rate from A to G and an increase in the mutation rate from C to T. However, neither a reduction in the strength of selection nor a change in the mutational pattern can alone explain all of the data observed in the D. melanogaster lineage. For example, we also confirm previous results showing that the Notch locus has experienced positive selection for previously classified unpreferred mutations.