What is the best way to reward innovation? While prizes avoid deadweight loss, intellectual property selects high social surplus projects. Optimal innovation policy thus trades off the ex-ante screening benefit and the ex-post distortion. It solves a multidimensional screening problem in the private information held by the innovator: research cost, quality and market size of the innovation. The appropriate degree of market power is never full monopoly pricing and is determined by measurable market characteristics, the inequality and elasticity of innovation supply, making the analysis open to empirical calibration. The framework has applications beyond IP policy to the optimal pricing of platforms or the optimal procurement of public infrastructure.