The analysis of evolutionary rates is a popular approach to characterizing the effect of natural selection at the molecular level. Sequences contributing to species adaptation are expected to evolve faster than nonfunctional sequences because favourable mutations have a higher fixation probability than neutral ones. Such an accelerated rate of evolution might be due to factors other than natural selection, in particular GC-biased gene conversion. This is true of neutral sequences, but also of constrained sequences, which can be illustrated using the mouse Fxy gene. Several criteria can discriminate between the natural selection and biased gene conversion models. These criteria suggest that the recently reported human accelerated regions are most likely the result of biased gene conversion. We argue that these regions, far from contributing to human adaptation, might represent the Achilles' heel of our genome.