There are a variety of synonyms for the phrase "dreaming sleeps." Some potential options include REM sleep, rapid eye movement sleep, or even simply "deep sleep." Other ways of referring to the state of dreaming can include phrases like "slumbering" or "dozing off," while more colloquial terms might include "catching z's," "getting shut-eye," or "snoozing." Depending on the context, certain phrases may be more appropriate than others. For example, a medical professional might use more specific terminology like "REM sleep" to discuss a patient's sleep patterns, while a friend might simply say that they spent the night "dreaming away".