I know that one night of sleep deprivation will be followed by REM rebound leading to increased dream activity. But does the REM rebound happen after TWO nights of sleep deprivation? For example, someone who sleeps 1 hour one night and 1 hour the night after that. Would that person have REM rebound happen on the third night?

I'm not sure that they would. Studies done on human beings and animals showed that people sleep more deeply after one night of sleep deprivation to make up for the lost sleep. But they don't sleep any more deeply after a second night of sleep deprivation. Studies show that people go back to sleeping normally after the second night of deprivation.

I think that means that REM rebound won't happen after two sleep deprived nights.

The reason I ask is because I only slept one hour last night. And after an unpleasant dream experience not too long ago, I'm looking to avoid the REM rebound. So I'm thinking that if I restrict myself to 1 hour of sleep again tonight, I'll be able to avoid the REM rebound tomorrow night.