The effect of napping versus wakefulness was studied on primed and repeated Remote Associate Tests (RATs) and on divergent creativity tests. The participants were 42 students from the USA, studying international courses at a Swedish university. The hypotheses for the RATs were (1), when the correct answers were primed before the nap, the RAT should be solved better for those who entered REM sleep, compared to those with no REM sleep or a resting condition; and (2), when retested the RAT should be solved better after a nap than after rest. For the creativity tests, hypothesis (3) was that creativity should be higher after the nap than after rest. Hypothesis 1 and hypothesis 3 were not supported. Hypothesis 2 was supported in an ANOVA. The REM group improved more than the rest group on the repeated RAT. Also, the No-REM and rest groups differed, strengthening the importance of both REM and No-REM sleep for creative problem-solving.