Wiktionary
half-asleep
a. Showing signs of being asleep or very sleepy, as not demonstrating full energy or attention.
Usage examples of "half-asleep".
Then Malone rang Russ Clements, who, half-asleep but still awake enough to be concerned for the Malone family, said only, 'Lisa and the kids all right?
She staggered, still half-asleep, to the corner cupboard and pulled a plain pink cotton shift down over her nude body.
He drew it, half-asleep, and later looked and found that his unconscious mind had designed a power-supply system which made Walden's look rather primitive.