We present a model of sequential innovation in which innovators use several research inputs to invent new goods. We extend work by Shapiro (2001) and Lerner and Tirole (2004) by studying the effects of increases in the number of patented research inputs on innovation incentives and optimal patent policy. We consider not only the effects on the incentives to invent final goods, but also on the incentives to invent research inputs (ex-ante effect). We find increasing complexity has a negative effect on innovation activity in the final goods sector when research inputs are complements. Either limiting market power through weaker patents or reducing the lack of coordination through patent pools may solve this problem. We also find the optimal patent breadth and show it is increasing in the elasticity of substitution between the inputs used in research and decreasing (increasing) in the complexity of the R&D process when research inputs are complements (substitutes).