U.S. housing voucher holders pay their landlord a fraction of household income and the government pays the rest, up to a rent ceiling. We study how two types of changes to the rent ceiling affect landlords and tenants. A policy that makes vouchers more generous across a metro area benefits landlords through increased rents, with minimal impact on neighborhood and unit quality. A second policy that indexes rent ceilings to neighborhood rents leads voucher holders to move in higher-quality neighborhoods with lower crime, poverty and unemployment.