During specific rapid eye movement (REM) sleep deprivation its homeostatic regulation is expressed by progressively more frequent attempts to enter REM and by a compensatory rebound after the deprivation ends. The buildup of pressure to enter REM may be hypothesized to depend just on the time elapsed without REM or to be differentially related to non-REM (NREM) and wakefulness. This problem bears direct implications on the issue of the function of REM and its relation to NREM. We compared three protocols that combined REM-specific and total sleep deprivation so that animals underwent similar 3-h REM deprivations but different concomitant NREM deprivations for the first 2 (2T1R), 1 (1T2R), or 0 (3R) hours. Deprivation periods started at hour 6 after lights on. Twenty-two chronically implanted rats were recorded. The median amount of REM during all three protocols was approximately 1 min. The deficits of median amount of NREM in minutes within the 3-h deprivation periods as compared with their baselines were, respectively for 2T1R, 1T2R, and 3R, 35 (43%), 25 (25%), and 7 (7%). Medians of REM rebound in the three succeeding hours, in minutes above baseline, were, respectively, 8 (44%), 9 (53%), and 9 (50%), showing no significant differences among protocols. Attempted transitions to REM showed a rising trend during REM deprivations reaching a final value that did not differ significantly among the three protocols. These results support the hypothesis that the build up of REM pressure and its subsequent rebound is primarily related to REM absence independent of the presence of NREM.