In most procedures I've observed (or experienced first-hand), a combo of Versed (a benzo) and a small amount of Propofol for the "milk of amnesia" effect is lumped under the term "conscious sedation".

The patient is aware, can breathe on their own, and can respond to basic commands, but is relaxed, with a much higher pain threshold, and has no memory of the event.

That sync with your experience, doc?