Creative thought relies on the reorganisation of existing knowledge. Sleep is known to be important for creative thinking, but there is a debate about which sleep stage is most relevant, and why. We address this issue by proposing that rapid eye movement sleep, or REM, and non-REM sleep facilitate creativity in different ways. Memory replay mechanisms in non-REM can abstract rules from corpuses of learned information, while replay in REM may promote novel associations. We propose that the iterative interleaving of REM and non-REM across a night boosts the formation of complex knowledge frameworks, and allows these frameworks to be restructured, thus facilitating creative thought. We outline a hypothetical computational model which will allow explicit testing of these hypotheses.