A positive correlation between ω, the ratio of the nonsynonymous and synonymous substitution rates, and dS, the synonymous substitution rate has recently been reported. This correlation is unexpected under simple evolutionary models. Here, we investigate two explanations for this correlation: first, whether it is a consequence of a statistical bias in the estimation of ω and second, whether it is due to substitutions at adjacent sites. Using simulations, we show that estimates of ω are biased when levels of divergence are low. This is true using the methods of Yang and Nielsen, Nei and Gojobori, and Muse and Gaut. Although the bias could generate a positive correlation between ω and dS, we show that it is unlikely to be the main determinant. Instead we show that the correlation is reduced when genes that are high quality in sequence, annotation, and alignment are used. The remaining--likely genuine--positive correlation appears to be due to adjacent tandem substitutions; single substitutions, though far more numerous, do not contribute to the correlation. Genuine adjacent substitutions may be due to mutation or selection.