We study efficient allocations and optimal policies in a Mirrleesean life-cycle economy with risky human capital accumulation and permanent ability differences. We assume that ability, labor supply, learning effort and returns to human capital are all private information of the agents. We show that the "no distortion at the top" result from the Mirrleesean literature may not apply if discouraging labor supply increases incentives to invest in human capital. We also show that, under certain conditions, the inverse of the intratemporal wedge follows a random walk, implying that the average intratemporal wedge increases over time. This result is, to our knowledge, novel. We calibrate a two-period economy and find several notable results. First, to elicit learning effort, it is efficient to make the consumption process risky for high-ability agents while insuring low-ability agents. Second, high-ability agents face the largest expected increase in the intratemporal wedge. Third, high-ability agents face a higher intertemporal wedge. These normative prescriptions differ significantly from the existing literature that abstracts from human capital. We also find large welfare gains for the U.S. from switching to an optimal tax system.