Public-private partnerships (PPPs) cannot be justified because they free public funds. When PPPs are desirable because the private sector is more efficient, the contract that optimally trades demand risk, user-fee distortions and the opportunity cost of public funds is characterized by a minimum revenue guarantee and a cap on the firm's revenues. Yet income guarantees and revenue sharing arrangements observed in practice differ fundamentally from those suggested by the optimal contract. The optimal contract can be implemented via a competitive auction with realistic informational requirements; and risk allocation under the optimal contract suggests that PPPs are closer to public provision than to privatization.