Although positive selection has been detected in many genes, its overall contribution to protein evolution is debatable. If the bulk of molecular evolution is neutral, then the ratio of amino-acid (A) to synonymous (S) polymorphism should, on average, equal that of divergence. A comparison of the A/S ratio of polymorphism in Drosophila melanogaster with that of divergence from Drosophila simulans shows that the A/S ratio of divergence is twice as high---a difference that is often attributed to positive selection. But an increase in selective constraint owing to an increase in effective population size could also explain this observation, and, if so, all genes should be affected similarly. Here we show that the difference between polymorphism and divergence is limited to only a fraction of the genes, which are also evolving more rapidly, and this implies that positive selection is responsible. A higher A/S ratio of divergence than of polymorphism is also observed in other species, which suggests a rate of adaptive evolution that is far higher than permitted by the neutral theory of molecular evolution.