This paper analyses the impact of farm productivity as well as farm size on deforestation in Brazil. A two step econometric approach is adopted. A bootstrapped translog stochastic frontier that is a posteriori checked for functional consistency is used in order to estimate technical efficiency of which estimates are introduced in a land use model to assess the impact of productivity and farm size on deforestation. Analysis of agricultural census tract data suggests that technical efficiency has a nonlinear (convex) effect: less and more efficient farms use more land for agricultural activities and so they have a positive effect on deforestation. However, the majority of farms are on the ascendant slope so that efficiency implies more deforestation in Brazilian Legal Amazon. Moreover, farm size has a robust negative effect on deforestation. Contrary to many studies, this result suggests that small farms convert more natural (forested) land into agricultural land than large ones