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The case for progressive income taxation is often based on the classic result of Jakobsson (1976) and Fellman (1976), according to which progressive and only progressive income taxes—in the sense of increasing average tax rates on income—ensure a reduction in income inequality. This result has been criticized on the ground that it ignores the possible disincentive effect of taxation on work effort, and the resolution of this critique has been a long-standing problem in public finance. This paper provides a normative rationale for progressivity that takes into account the effect of an income tax on labor supply. It shows that a tax schedule is inequality reducing only if it is progressive—in the sense of increasing marginal tax rates on income, and identifies a necessary and sufficient condition on primitives under which progressive and only progressive taxes are inequality reducing.