We investigate the extent by which the estimates of the rate of adaptive molecular evolution obtained by extending the McDonald-Kreitman test are biased if the species, subjected to analysis, diverged recently. We show that estimates can be biased if the nucleotide divergence between the species is low relative to within species variation, and that the magnitude of the bias depends on the rate of adaptive evolution and the distribution of fitness effects of new mutations. Bias appears to be because of three factors: (1) misattribution of polymorphism to divergence; (2) the contribution of ancestral polymorphism to divergence; and (3) different rates of fixation of neutral and advantageous mutations. If there is little adaptive molecular evolution, then slightly deleterious mutations inflate estimates of the rate of adaptive evolution, because these contribute proportionately more to polymorphism than to nucleotide divergence than neutral mutations. However, if there is substantial adaptive evolution, polymorphism contributing to apparent divergence may downwardly bias estimates. We propose a simple method for correcting the different contributions of slightly deleterious and neutral mutations to polymorphism and divergence, and apply it to datasets from several species. We find that estimates of the rate of adaptive molecular evolution from closely related species may be underestimates by ~10% or more. However, after the contribution of polymorphism to divergence is removed, the rate of adaptive evolution may still be overestimated as a consequence of ancestral polymorphism and time for fixation effects. This bias may be substantial if branch lengths are less than 10N (e) generations.