We determine optimal labor-income and capital taxes in a world with both income inequality and inequality in health outcomes. We do so by introducing mortality risk into a two-period life-cycle model of optimal taxation. Higher longevity implies a greater need for future consumption, and therefore a greater need for savings. We show that this generates a reason to tax savings if high-ability individuals expect to live longer than low-ability individuals -- a well-documented empirical regularity. Intuitively, savings provide information about an individual's longevity, and therefore about his or her underlying ability. As a result, a tax on savings allows the government to redistribute income more efficiently. We show that this finding is robust to the presence of various informational asymmetries within the private annuity market, as long as there is free entry of annuity providers.