Firms and governments often use R&D contests to incentivize suppliers to develop and deliver innovative products. The optimal design of such contests depends on empirical primitives: the cost of research, the uncertainty in outcomes, and the surplus participants capture. Can R&D contests in real‐world settings be redesigned to increase social surplus? I ask this question in the context of the Department of Defense's Small Business Innovation Research program, a multistage R&D contest. I develop a structural model to estimate the primitives from data on R&D and procurement contracts. I find that the optimal design substantially increases social surplus, and simple design changes in isolation (e.g., inviting more contestants) can capture up to half these gains; however, these changes reduce the DOD's own welfare. These results suggest there is substantial scope for improving the design of real‐world contests but that a designer must balance competing objectives.