This paper investigates the relative economic and environmental outcomes of price versus quantity mechanisms to control GHG emissions when abatement costs are uncertain. In particular, we evaluate the impacts on policy costs, CO2 emissions and energy R&D for a stringent mitigation target of 550 ppmv CO2 equivalent (i.e. 450 for CO2 only) concentrations. The analysis is performed in an optimal growth framework via Monte Carlo simulations of the integrated assessment model WITCH (World Induced Technical Change Hybrid). Results indicate that the price instrument stochastically dominates the quantity instrument when a stringent stabilization policy is in place.