We study the optimal design of means-tested transfers and progressive income taxes. In a simple analytical model, we demonstrate an optimally negative relation between transfers and income-tax progressivity due to efficiency and redistribution concerns. In a rich dynamic model, we quantify the optimal plan with flexible tax-and-transfer functions. Transfers should be larger than currently in the U.S. and financed with moderate income-tax progressivity. Transfers are key to implement higher progressivity in average than in marginal tax-and-transfer rates, achieving redistribution while preserving efficiency. Quantitatively, the left tail of the income distribution determines optimal transfers, whereas the right tail determines income-tax progressivity.