How can REDD credits be included in a future global carbon market, and what are the impacts of inclusion? We analyze ten different scenarios through 2020, varying the global emission caps and the REDD rules. An inclusion of REDD credits without any adjustments in the global cap will lower carbon prices significantly and cause crowding out. The cap must move towards the 2 degrees climate target if REDD inclusion is to maintain high carbon prices and strong incentives for emissions reductions in other sectors. At the same time, reaching the 2 degree target without full REDD inclusion will increase global mitigation costs by more than 50%.