Can evolvability itself be the product of adaptive evolution? To answer this question is challenging, because any DNA mutation that alters only evolvability is subject to indirect, "second order" selection on the future effects of this mutation. Such indirect selection is weaker than "first-order" selection on mutations that alter fitness, in the sense that it can operate only under restrictive conditions. Here I discuss a route to adaptive evolvability that overcomes this challenge. Specifically, a recent evolution experiment showed that some mutations can enhance both fitness and evolvability through a combination of direct and indirect selection. Unrelated evidence from gene duplication and the evolution of gene regulation suggests that mutations with such dual effects may not be rare. Through such mutations, evolvability may increase at least in part because it provides an adaptive advantage. These observations suggest a research program on the adaptive evolution of evolvability, which aims to identify such mutations and to disentangle their direct fitness effects from their indirect effects on evolvability. If evolvability is itself adaptive, Darwinian evolution may have created more than life's diversity. It may also have helped create the very conditions that made the success of Darwinian evolution possible.