Electroencephalographic (EEG) δ waves during non-rapid eye movement sleep (NREMS) after sleep deprivation are enhanced. That observation eventually led to the use of EEG δ power as a parameter to model process S in the two-process model of sleep. It works remarkably well as a model parameter because it often co-varies with sleep duration and intensity. Nevertheless there is a large volume of literature indicating that EEG δ power is regulated independently of sleep duration. For example, high amplitude EEG δ waves occur in wakefulness after systemic atropine administration or after hyperventilation in children. Human neonates have periods of sleep with an almost flat EEG. Similarly, elderly people have reduced EEG δ power, yet retain substantial NREMS. Rats provided with a cafeteria diet have excess duration of NREMS but simultaneously decreased EEG δ power for days. Mice challenged with influenza virus have excessive EEG δ power and NREMS. In contrast, if mice lacking TNF receptors are infected, they still sleep more but have reduced EEG δ power. Sleep regulatory substances, e.g., IL1, TNF, and GHRH, directly injected unilaterally onto the cortex induce state-dependent ipsilateral enhancement of EEG δ power without changing duration of organism sleep. IL1 given systemically enhances duration of NREMS but reduces EEG δ power in mice. Benzodiazepines enhance NREMS but inhibit EEG δ power. If duration of NREMS is an indicator of prior sleepiness then simultaneous EEG δ power may or may not be a useful index of sleepiness. Finally, most sleep regulatory substances are cerebral vasodilators and blood flow affects EEG δ power. In conclusion, it seems unlikely that a single EEG measure will be reliable as a marker of sleepiness for all conditions.