Half asleep. Synonyms:drowsing, drowsy."It seemed a pity to disturb the drowsing (or dozing) professor" , "A tired dozy child" , "The nodding (or napping) grandmother in her rocking chair"
... hush all about. The bubbling ecstasy of a bobolink floated above the grasses of a meadow, and near at hand a wren hopped about in the alders and chirped dozy notes. Peace and restfulness brooded. The man at the brook leaned low and thrust his head into the water and then rose and shook the drops from his thick thatch of brown hair. He did it with a sort of canine wriggle ... — The Landloper - The Romance Of A Man On Foot • Holman Day