Art by smbc-comics
Consciousness is often said to disappear in deep, dreamless sleep. We argue that this assumption is oversimplified. Unless dreamless sleep is defined as unconscious from the outset there are good empirical and theoretical reasons for saying that a range of different types of sleep experience, some of which are distinct from dreaming, can occur in all stages of sleep.
Pubmed Articles
Does Consciousness Disappear in Dreamless Sleep?
Sciencealert Article We Were Wrong About Consciousness Disappearing in Dreamless Sleep, Say Scientists
That there are more than one definition is kind of the problem. And that you'd characterize any of them as "good" sounds more like a euphemism for "good enough for a particular scenario."