The delta integrated amplitude (DIA) in nonrapid eye movement period 1 (NREMP1) of daytime naps was precisely subtracted from the NREMP1s of ensuing nocturnal sleep, indicating that the brain can retain a record of DIA expressed in sleep episodes initiated 12.5 and 8.5 hours before nocturnal sleep onset. The DIA subtraction was primarily accomplished by reduced NREMP1 duration [earlier rapid eye movement (REM) onset], suggesting that the timing of REM period 1 (REMP1) onset is controlled by delta need. This result is consistent with the hypothesis that REM sleep occurs when a stimulus for NREM has been partially depleted.