This paper examines the effects of firm-level innovation in carbon-abatement technologies on optimal cap-and-trade schemes with and without price controls. We characterize optimal cap-and-trade regulation with a price cap and a price floor, and compare it to the special cases of pure taxation and a simple emissions cap. Innovation shifts the tradeoff between price- and quantity-based instruments towards quantity-based emissions trading schemes. More specifically, an increase in innovation effectiveness lowers the optimal emissions cap, and leads to relaxed price controls unless the slope of the marginal environmental damage curve is small. Because of the decrease in the emissions cap, innovation in abatement technologies can lead to a higher expected carbon price, so as to provide sufficient incentives for private R&D investments. The expected carbon price decreases once innovative technologies are widely used.