If you drowse, you are almost asleep or just asleep. Nina drowsed for a while. = doze. to be in a light sleep or to feel as though you are almost asleep (drowsy)
half asleep; "made drowsy by the long ride"; "it seemed a pity to disturb the drowsing (or dozing) professor"; "a tired dozy child"; "the nodding (or napping) grandmother in her rocking chair"