This paper examines the sensitivity of the growth-inequality tradeoff to the progressivity of the tax structure. Using an endogenous growth model calibrated to approximate the US tax structure, we simulate a 5% reduction in the economy-wide average tax rate attained by alternative combinations of a reduction in the base tax rate and an increase in progressivity. In all cases the dynamic responses across income classes are diverse. With fixed progressivity the tax benefits favor the poorer quintiles, but the richest quintile is the only group that increases its relative share of capital and income. The net long-run effect is a mild increase in the overall growth rate, accompanied by a substantial increase in inequality. Restructuring the tax cut by allowing a larger reduction in the base tax rate coupled with a large increase in progressivity, designed to maintain the tax burden on the richest quintile unchanged, the exact opposite responses emerge; growth and inequality both decline. By judicious choice of the crucial fiscal parameters, the tax cut can be structured so that the growth rate increases while inequality simultaneously declines. The required structural changes are small, highlighting the extreme sensitivity of the tradeoff to the degree of tax progressivity.