The Collaborative International Dictionary of English v.0.48:

drowsiness \drow"si*ness\, n.
   State of being drowsy. --Milton.
   [1913 Webster]

WordNet (r) 3.0 (2006):

drowsiness
    n 1: a very sleepy state; "sleepiness causes many driving
         accidents" [syn: sleepiness, drowsiness, somnolence]
         [ant: sleeplessness, wakefulness]

Moby Thesaurus II by Grady Ward, 1.0:

48 Moby Thesaurus words for "drowsiness":
   acedia, apathy, boredom, doziness, dullness, enervation, ennui,
   fatigue, heaviness, hebetude, inanimation, indifference, jadedness,
   lackadaisicalness, languidness, languishment, languor,
   languorousness, lassitude, lenitude, lentor, lethargy,
   lifelessness, listlessness, oscitancy, oscitation, pandiculation,
   passivity, phlegm, satedness, sleepiness, sloth, slothfulness,
   slowness, sluggishness, somnolence, somnolency, stretching,
   stupefaction, stupor, supineness, torpidity, torpidness, torpitude,
   torpor, weariness, world-weariness, yawning