Modularity has been heralded as an organizational and technical architecture that enhances incremental and modular innovation. Less attention has been paid to the possible implications of modular architectures for imitation. To understand the implications of modular designs for competitive advantage, one must consider the dual impact of modularity on innovation and imitation jointly. In an attempt to do so, we set up three alternative structures that vary in the extent of modularity and hence in the extent of design complexity: nonmodular, modular, and nearly modular designs. In each structure, we examine the trade-offs between innovation benefits and imitation deterrence. The results of our computational experiments indicate that modularization enables performance gains through innovation but, at the same time, sets the stage for those gains to be eroded through imitation. In contrast, performance differences between the leaders and imitators persist in the nearly modular and the nonmodular structures. Overall, we find that design complexity poses a significant trade-off between innovation benefits (i.e., generating superior strategies that create performance differences) and imitation deterrence (i.e., preserving the performance differences). We also examine the robustness of our results to variations in imitation accuracy. In addition to documenting the overall robustness of our principal finding, the ancillary analyses provide a more nuanced rendering of the relationship between the architecture of complexity and imitation efforts.