There are various synonyms for the phrase "got some shut-eye." Some common alternatives include "slept," "dozed off," "caught some Zs," "took a nap," "hit the hay," "crashed," "nodded off," "snoozed," and "snatched some sleep." Each of these phrases can convey a slightly different meaning, depending on the context. For instance, "slept" may be used in more formal contexts or to describe a longer period of rest, while "nodded off" is more informal and may suggest a shorter nap or moment of drowsiness. Overall, these synonyms provide a great way to add variety and expressiveness to our language!