The current paper aims to assess the credibility of demand-side policies to curb deforestation. We tackle this question focusing on the Brazilian soy sector, as conversion from forests to soyproducing areas is a major driver of deforestation. We estimate a firm-level gravity model relating soy exports to destination-specific soy demand. First, we estimate a positive elasticity of soy exports to foreign demand, which confirms the credibility of demand-side policies. Second, we document that the average response hides significant heterogeneities across exporters and across municipalities. Combining export elasticities with soy expansion possibilities, demand-side policies could hence avoid aggregate deforestation, particularly in regions proximate to the Amazon.