It is unknown if resting sharks can sleep, which is also true for gliding ones. Here, a videotaped bull shark is presented that drifted in an uncontrolled manner for 120 seconds while sinking with 0.1 m/second. Several aspects are discussed to determine if the shown behavior reflects the commonly accepted definition of sleep. Additionally, the idea is also discussed if this state might reflect a “quiet waking state” instead of where the shark still maintained some vigilance despite its general appearance.