When competition increases, it is often presumed that public schools will be forced to become more efficient. This paper challenges that presumption, showing that in well-defined circumstances, rent-seeking public schools find it optimal to reduce productivity when a voucher is introduced. This occurs for incentive reasons alone. More generally, the productivity effects of vouchers are shown to be non-uniform, varying systematically according to the distribution of households and the form the voucher takes; when the voucher is targeted, perverse productivity outcomes do not arise. The analysis has relevance to the policy issue of voucher design.