Implications of income uncertainty for socially efficient redistribution are examined in a utilitarian framework. Counterintuitively, a policymaker may respond optimally to a negative utility shock in the economy by redistributing income away from those who suffered the shock. Holding expected income constant, it may be welfare-enhancing to redistribute income away from risk-averse taxpayers who suffer an increase in the variance of their earnings. The direction of redistribution following an increase in uncertainty depends on the degree to which absolute risk aversion declines with consumption. A condition is provided for when an efficient policy redistributes away from those facing the greatest uncertainty.