Governments often subsidize private R&D through a mix of interdependent mechanisms, but how these subsidies interact is not well understood. This paper shows that direct subsidies (grants) and indirect subsidies (tax credits) for R&D are complements for small firms but substitutes for larger firms on the intensive margin. Using non-overlapping funding rules and policy changes in the UK, I find that a large increase in tax credit generosity nearly doubles the positive effect that grants have on R&D expenditures for small firms, but it cuts the effect in half for larger firms. The policy interactions also influence the types of innovations that emerge: small firms steer grant funding more towards horizontal innovation efforts with increased tax credit rates, while larger firms substitute funds away from them. I explore the mechanism behind the results and provide suggestive evidence that subsidy complementarity for small firms is consistent with these firms facing financial constraints, whereas for larger firms, tax credits may fund infra-marginal projects.