Millions of patients are admitted each year to intensive care units (ICUs) in the United States. A significant fraction of ICU survivors develop life-long cognitive impairment, incurring tremendous financial and societal costs. Delirium, a state of impaired awareness, attention and cognition that frequently develops during ICU care, is a major risk factor for post-ICU cognitive impairment. Recent studies suggest that patients experiencing electroencephalogram (EEG) burst suppression have higher rates of mortality and are more likely to develop delirium than patients who do not experience burst suppression. Burst suppression is typically associated with coma and deep levels of anesthesia or hypothermia, and is defined clinically as an alternating pattern of high-amplitude "burst" periods interrupted by sustained low-amplitude "suppression" periods. Here we describe a clustering method to analyze EEG spectra during burst and suppression periods. We used this method to identify a set of distinct spectral patterns in the EEG during burst and suppression periods in critically ill patients. These patterns correlate with level of patient sedation, quantified in terms of sedative infusion rates and clinical sedation scores. This analysis suggests that EEG burst suppression in critically ill patients may not be a single state, but instead may reflect a plurality of states whose specific dynamics relate to a patient's underlying brain function.