Comparison of 317 gene pairs in human and mouse that were duplicated after the most recent common ancestor of the two species was used to search for candidates that may have undergone functional differentiation. Even when corrected for multiple tests, Tajima's relative rate test showed significant rate differences in 36% of cases for which the test was applicable. However, a significant result in this case was increasingly likely as the sequence length increased; thus, a statistically significant result of a relative rate test may not be biologically meaningful. We used regression methods to provide more robust methods of testing for functionally differentiated gene pairs, which take into account the variation in the entire data set by examination of residuals from regression-identified gene pairs with unusually high nonsynonymous divergence from a reference sequence and from each other. This approach identified six duplicate gene pairs that appeared to be candidates for functional differentiation as a result of positive Darwinian selection.