This paper develops a framework for testing discrete complementarities in innovation policy using European data on obstacles to innovation. We propose a discrete test of supermodularity in innovation policy leading to a number of inequality constraints. We apply our test to two types of innovation decisions: to innovate or not, and if so, by how much. We find that industries display a considerable amount of complementarity, with some industries being complementary across all obstacles. We also find that the lack internal human capital (skilled personnel) is complementary to all the other obstacles in almost all industries. In this sense, our results suggest that internal human capital is key for any innovation policy, insofar that it is complementary to all the other factors that might hamper innovation activities. We like to thank Dietmar Harhoff, Bernard Sinclair-Desgagne, and David Soskice for their detailed comments. We also like to thank Susan Athey, Astrid Jung, and Jacques Mairesse, as well as the participants of the WZB-Cirano workshop on "Innovation and Supermodularity", June 15-17, Montreal.