We ask: what are the most efficient means of redistribution in an unequal society? We answer this question by characterizing the optimal shape of non-linear income and wealth taxes in a dynamic general equilibrium model with uninsurable idiosyncratic risk. Our analysis reproduces the distribution of income and wealth in the United States and explicitly takes into account the long-lived transition dynamics after policy reforms. We find that a uniform flat tax on capital and labor income combined with a lump-sum transfer is nearly optimal. Though taxing wealth and allowing for increasing marginal income tax schedules raises utilitarian welfare, the incremental gains from doing so are small. This result is robust to changing household preferences, the distribution of ability, the planner’s preference for redistribution, as well as to explicitly modeling private business ownership and the ensuing heterogeneity in rates of return across financially constrained entrepreneurs.