Gotten some shut eye is a common colloquialism used to refer to the act of sleeping. However, there are many synonyms for this phrase that can be used to add more variety and interest to your writing. Some alternatives to gotten some shut-eye include catching some Z's, dozing off, hitting the hay, snoozing, sleeping soundly, napping, drifting off, resting one's eyes, and taking a cat nap. Each of these idioms can be used to add a colorful description of sleep that will keep your writing more intriguing and lively. So, if you need to write about sleep, consider using one of these synonyms instead of the same, tired old phrase.