Energy efficiency is a key component of climate policy. We study micro and macro rebound effects after the introduction of energy-efficient biomass cookstoves (EEBCs). We develop a model of biomass supply and demand in rural Africa. The impact of EEBCs is empirically explored in Rwanda where we randomly varied subsidy levels for EEBCs at the village-level. Demand is price elastic, so we exploit exogenous saturation variation to study local rebound effects. While adoption of EEBCs reduces household firewood consumption, we find no meaningful local rebound effects and identify conditions under which this finding generalizes to other settings - or not.