drowse

from The American Heritage® Dictionary of the English Language, 5th Edition.

• intransitive verb To be half-asleep.
• intransitive verb To make drowsy.
• intransitive verb To pass (time) by drowsing.
• noun The condition of being sleepy.

from The Century Dictionary.

• To be heavy with sleepiness; be half asleep; hence, to be heavy or dull.
• Synonyms Doze, Slumber, etc. See sleep
• noun A state of somnolency; a half-sleep.

from the GNU version of the Collaborative International Dictionary of English.

• transitive verb To make heavy with sleepiness or imperfect sleep; to make dull or stupid.
• noun A slight or imperfect sleep; a doze.
• intransitive verb To sleep imperfectly or unsoundly; to slumber; to be heavy with sleepiness; to doze.

from Wiktionary, Creative Commons Attribution/Share-Alike License.

• noun The state of being sleepy and inactive.
• verb intransitive To be sleepy and inactive (also figurative).
• verb intransitive To nod off; to fall asleep.
• verb transitive To advance drowsily. (Used especially in the phrase "drowse one's way" ⇒ sleepily make one's way.)

from WordNet 3.0 Copyright 2006 by Princeton University. All rights reserved.

• verb be on the verge of sleeping
• verb sleep lightly or for a short period of time
• noun a light fitful sleep