This paper studies the optimal design of R D contests. A sponsor (e.g. the US Department of Defense or the World Health Organization) wants to improve the quality of the winning products. To do so, it partitions its budget between two schemes: an inducement prize and efficiency-enhancing subsidies to the firms competing in the contest. Prizes and subsidies have different functions, and they provide complementary incentives. In the optimally designed contest, subsidies increase while the prize decreases, if the innovation process is more challenging. Further, sensible conditions are identified under which the optimal contest implements either a handicapping scheme (by preferentially subsidizing the underdog ) or a national champion scheme (by favoring the favorite ). Our analysis yields a number of useful implications and sheds light on an array of R D incentive schemes, such as the DoD s design competitions and vaccine development incentives.