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 incometaxes in the sense of increasing average tax rates on income ensure a reduction in incomeinequality. This result has been criticized on the ground that it ignores the possibledisincentive effect of taxation on work effort, and the resolution of this critique has beena long-standing problem in public finance. This paper provides a normative rationale forprogressivity that takes into account the effect of an income tax on labor supply. It showsthat a tax schedule is inequality reducing only if it is progressive in the sense of increasingmarginal tax rates on income, and identifies a necessary and sufficient conditionon primitives under which progressive and only progressive taxes are inequality reducing.