Reducing Emissions from Deforestation and Forest Degradation (REDD+) has become a central dimension of the contemporary international forest regime. The mechanism seeks to reward actors for keeping or restoring forests as a means to reduce carbon emissions. Carbon rights, here understood as title to carbon credits, have an odd status in the REDD+ debate. They are closely associated with the belief that REDD+ will generate (economic) ''rents'' - i.e. revenues exceeding the full cost of the corresponding effort - which means framing the discussion in terms of entitlement to revenues beyond mere financial compensations. We suggest that, in an ''ideal'' REDD+ scheme, the possibility of obtaining rents in REDD+ would be very limited. In the real world, rent could be created by strategic behaviours by setting a reference emission level (what would occur under a business-asusual scenario) and by possible acceptance, for political reasons, of inappropriate rules such as being remunerated for the full stock of carbon. The carbon rights rhetoric leads to rent- seeking since remunerations could be disconnected from the active contribution to the production of emission reductions, which is a public good by nature. Another interpretation of carbon rights is the right to benefit from the sale of carbon credits, a framework within which what is at stake is sharing the benefits deriving from the human production and the sale of these benefits, a traditional social issue. In this case, we argue, the concept of carbon rights is useless and even misleading. Compensating for easements would be a more appropriate framework for designing incentive schemes such as payments for environmental services (PES). Reforming land tenure codes to allow individuals, families and communities to claim property or collective tenure rights on the land and the trees is the issue that matters in order to start tackling fairness in REDD+ and PES initiatives.