Tropical deforestation for agriculture causes alarming CO2 emissions and loss of biodiversity and ecosystem services. To prevent this, various governments and multinational commodity-buyers offer a positive incentive for locals conditional on no deforestation in a specified area. As an alternative to the area no-deforestation condition, we propose a weaker “regeneration condition”: if forest is cleared on land in the specified area, locals prevent its economic use, enabling the forest to regenerate. With innovation in cooperative game theory, we characterize the best condition (area no-deforestation vs. area regeneration) and feasible incentives to prevent deforestation and to compensate each local for his missed economic opportunity. The regeneration condition is best in an area with the potential for entrants to engage in deforestation. Without entrants, if locals can cooperate, the area no-deforestation condition is best, and works with any incentive that is more valuable for locals collectively than deforestation. By surveying smallholder palm farmers in 58 villages of East Kalimantan, Indonesia, we fit our model with a price premium for palm fruit as the incentive, in each village as the area. A price premium is an imperfect incentive, having least value for a farmer with the least land and, correspondingly, high temptation to engage in deforestation. The Roundtable on Sustainable Palm Oil (RSPO) price premium is too low. Still, with a moderate price premium, our area regeneration condition prevents deforestation in most villages and is remarkably robust to deter potential entrants.