In a recent electroencephalography (EEG) sleep study inspired by complexity theories of consciousness, we found that multi-channel signal diversity progressively decreased from wakefulness to slow wave sleep, but failed to find any significant difference between dreaming and non-dreaming awakenings within the same sleep stage (NREM2). However, we did find that multi-channel Lempel-Ziv complexity (LZC) measured over the posterior cortex increased with more perceptual ratings of NREM2 dream experience along a thought-perceptual axis. In this follow-up study, we re-tested our previous findings, using a slightly different approach. Partial sleep-deprivation was followed by evening sleep experiments, with repeated awakenings and immediate dream reports. Participants reported whether they had been dreaming, and were asked to rate how diverse, vivid, perceptual, and thought-like the contents of their dreams were. High density (64 channel) EEG was recorded throughout the experiment, and mean single-channel LZC was calculated for each 30 s sleep epoch. LZC progressively decreased with depth of non-REM sleep. Surprisingly, estimated marginal mean LZC was slightly higher for NREM1 than for wakefulness, but the difference did not remain significant after adjusting for multiple comparisons. We found no significant difference in LZC between dream and non-dream awakenings, nor any significant relationship between LZC and subjective ratings of dream experience, within the same sleep stage (NREM2). The failure to reproduce our own previous finding of a positive correlation between posterior LZC and more perceptual dream experiences, or to find any other correlation between brain signal complexity and subjective experience within NREM2 sleep, raises the question of whether EEG LZC is really a reliable correlate of richness of experience as such, within the same sleep stage.