The Cancún Agreements provide strong backing for a REDD+ (Reducing Emissions from Deforestation and Forest Degradation) mechanism whereby developed countries pay developing ones for forest conservation1. REDD+ has potential to simultaneously deliver cost-effective climate change mitigation and human development2, 3, 4, 5. However, most REDD+ analysis has used coarse-scale data, overlooked important opportunity costs to tropical forest users4, 5 and failed to consider how to best invest funds to limit leakage, that is, merely displacing deforestation6. Here we examine these issues for Tanzania, a REDD+ country, by comparing district-scale carbon losses from deforestation with the opportunity costs of carbon conservation. Opportunity costs are estimated as rents from both agriculture and charcoal production (the most important proximate causes of regional forest conversion7, 8, 9). As an alternative we also calculate the implementation costs of alleviating the demand for forest conversion--thereby addressing the problem of leakage--by raising agricultural yields on existing cropland and increasing charcoal fuel-use efficiency. The implementation costs exceed the opportunity costs of carbon conservation (medians of US6.50 versus US3.90 per Mg CO2), so effective REDD+ policies may cost more than simpler estimates suggest. However, even if agricultural yields are doubled, implementation is possible at the competitive price of ar126US12 per Mg CO2