The efficiency of publicly-subsidized, privately-provisioned social insurance programs depends on the interaction between strategic insurers and the subsidy mechanism. We study this interaction in the context of Medicare's prescription drug coverage program. We find that the observed mechanism is successful in keeping "raise-the-subsidy" incentives relatively low, acts much like a flat voucher, and obtains a level of welfare close to the optimal voucher. Across a range of counterfactuals, we find that more efficient subsidy mechanisms share three features: they retain the marginal elasticity of demand, limit the exercise of market power, and preserve the link between prices and marginal costs.