We use data on health plan choices by employees of Harvard University to compare the benefits of insurance competition with the costs of adverse selection. Moving to a voucher-type system induced significant adverse selection, with a welfare loss of 2 to 4 percent of baseline spending. But increased competition reduced Harvard's premiums by 5 to 8 percent. The premium reductions came from insurer profits, so while Harvard was better off, the net effect for society was only the adverse selection loss. Adverse selection can be minimized by adjusting voucher amounts for individual risk. We discuss how such a system would work.