Simultaneity between prisoner populations and crime rates makes it difficult to isolate the causal effect of changes in prison populations on crime. To break that simultaneity, this paper uses prison overcrowding litigation in a state as an instrument for changes in the prison population. The resulting elasticities are two to three times greater than those of previous studies. A one-prisoner reduction is associated with an increase of fifteen Index I crimes per year. While calculations of the costs of crime are inherently uncertain, it appears that the social benefits associated with crime reduction equal or exceed the social costs of incarceration for the marginal prisoner.