Longman Dictionary of Contemporary English
Douglas Harper's Etymology Dictionary
n. (context informal English) sleep.
Usage examples of "shut-eye".
Worn-out babies cried incessantly, and a Hindi pop tune blared over the din, showing little consideration for those unlucky travelers hoping to catch a little shut-eye before boarding their planes, and the spicy scent of hot chai tea rose from more than one cup or thermos bottle clutched in the grip of a prospective passenger.
He stretches, eyeballs the whitewash wall to let the shadowplay run to its conclusion without shut-eye projection.