The paper aims at assessing discrete complementarities in innovation policies in the context of the Brazilian industry in 2003. The paper considers the approach advanced by Mohnen and and Röller [European Economic Review, 2005] that focuses on supermodularity and submodularity tests for obstacles to innovation (in the present application: lack of finance sources, lack of skilled personnel, lack of cooperation opportunities and lack of information on technology or markets). The application avoids micro-aggregation of the data and explicitly considers sampling weights in the econometric estimation. The analysis highlights the two phases of the innovation process in terms of the propensity and intensity of innovation. The evidence, unlike previous evidence, is not totally clear cut in terms of contrasts of the two phases. Nevertheless one can detect some substitutability and complementarity for specific pairs of obstacles in analysing the propensity to innovate, and strong evidence of complementarities in obstacles when considering the intensity of innovation. In the latter case, therefore, the evidence is suggestive and favours the adoption of more targeted incentive policies.