This paper provides empirically implementable sufficient statistics formulas for optimal nonlinear tax systems in the presence of  across-income heterogeneity in preferences, inheritances, income-shifting capabilities, and other sources. We characterize optimal smooth tax systems on income and savings (or other commodities), as well as simpler tax systems. We use familiar elasticity concepts and a novel sufficient statistic for heterogeneity correlated with earnings ability: the difference between  across-income variation in savings and the causal effect of income on savings. We apply these formulas to the United States and find that the optimal savings tax is mostly positive and progressive.