In this article, we consider the probabilistic identification of amino acid positions that evolve under positive selection as a multiple hypothesis testing problem. The null hypothesis "H0,s: site s evolves under a negative selection or under a neutral process of evolution" is tested at each codon site of the alignment of homologous coding sequences. Standard hypothesis testing is based on the control of the expected proportion of falsely rejected null hypotheses or type-I error rate. As the number of tests increases, however, the power of an individual test may become unacceptably low. Recent advances in statistics have shown that the false discovery rate--in this case, the expected proportion of sites that do not evolve under positive selection among those that are estimated to evolve under this selection regime--is a quantity that can be controlled. Keeping the proportion of false positives low among the significant results generally leads to an increase in power. In this article, we show that controlling the false detection rate is relevant when searching for positively selected sites. We also compare this new approach to traditional methods using extensive simulations.