As whales and dolphins switch off only a single hemisphere of the brain during their sleep. So that no possible attack escapes them.
To ducks mallards, when we have a nap, we stay when even on the watch. These animals close an eye but always keep the other one opened, what allows them to watch the arrival of a possible predator. Moreover, when they sleep in a row, mallards situated in both extremities always have the eye turned to the open outside.
This peculiarity is due to their sleep " unihémisphérique ", appropriate also for cetaceans: that is only a cerebral hemisphere falls asleep at the same time, by alternation, whereas the other rest on the alert.