We assess the usefulness of stochastic redistribution among a continuum of riskaverse agents with quasilinear utilities in labor. Agents differ according to their consumption tastes, which remain private information. We identify circumstances where stochastic redistribution is socially dominated by the deterministic policy where aftertax income lotteries are replaced with their certainty equivalent. We also provide a parametric example where feasible and incentive compatible lotteries locally dominate the optimal deterministic menu. In this example the downward pattern of incentives prevailing in the deterministic case is reversed to an upward pattern in the stochastic case.