This paper analyses how income redistribution affects inequality in a society in which individuals differ in their earning abilities and their preferences for consumption and leisure. After discussing the shortcomings of various standard approaches, I measure inequality in such a heterogeneous society by the inequality in individuals' so-called equivalent wages. This approach suggests that redistribution tends to reduce inequality by transferring income from high-ability to low-ability individuals, but to increase inequality by transferring income from consumption-loving to leisure-loving individuals. These countervailing effects lead in all my simulations to a U-shaped relationship between redistribution and inequality.