REDD (reduced emissions from deforestation and degradation) aims to slow carbon releases caused by forest disturbance by making payments conditional on forest quality over time. Like earlier policies to slow deforestation, REDD must change the behaviour of forest degrading actors. Broadly, it can be implemented with payments to forest users in exchange for improved forest management, thus creating incentives; through payments for enforcement, thus creating disincentives; or through addressing external drivers such as urban charcoal demand. In Tanzania, community‐based forest management (CBFM), a form of participatory forest management, was chosen by the Tanzania Forest Conservation Group, a local NGO, as a model for implementing REDD pilot programmes. Payments are made to villages that have the rights to forest carbon. In exchange, the villages must demonstrably reduce deforestation at the village level. In this paper, using this pilot programme as a case study, combined with a review of the literature, we provide insights for REDD implementation in sub‐Saharan Africa. We pay particular attention to leakage, monitoring and enforcement. We suggest that implementing REDD through CBFM‐type structures can create appropriate incentives and behaviour change when the recipients of the REDD funds are also the key drivers of forest change. When external forces drive forest change, however, REDD through CBFM‐type structures becomes an enforcement programme with local communities rather than government agencies being responsible for the enforcement. That structure imposes costs on local communities, whose local authority limits the ability to address leakage outside the particular REDD village.