Estimation of natural selection on protein-coding sequences is a key comparative genomics approach for de novo prediction of lineage-specific adaptations. Selective pressure is measured on a per-gene basis by comparing the rate of nonsynonymous substitutions to the rate of synonymous substitutions. All published codon substitution models have been time-reversible and thus assume that sequence composition does not change over time. We previously demonstrated that if time-reversible DNA substitution models are applied in the presence of changing sequence composition, the number of substitutions is systematically biased towards overestimation. We extend these findings to the case of codon substitution models and further demonstrate that the ratio of nonsynonymous to synonymous rates of substitution tends to be underestimated over three data sets of mammals, vertebrates, and insects. Our basis for comparison is a nonstationary codon substitution model that allows sequence composition to change. Goodness-of-fit results demonstrate that our new model tends to fit the data better. Direct measurement of nonstationarity shows that bias in estimates of natural selection and genetic distance increases with the degree of violation of the stationarity assumption. Additionally, inferences drawn under time-reversible models are systematically affected by compositional divergence. As genomic sequences accumulate at an accelerating rate, the importance of accurate de novo estimation of natural selection increases. Our results establish that our new model provides a more robust perspective on this fundamental quantity.