half story

a usable living space within a sloping roof, usually having dormer windows for lighting.

Origin of half story

First recorded in 1610–20

The half-story at the summit is ornamented with a row of arches, supported by pilasters.

The Pictureque Antiquities of Spain; |Nathaniel Armstrong Wells
Olive rose suddenly, silently declined her mother's aid, and went alone to their chamber in the half-story.

Madame Delphine |George W. Cable
A wonderful thing about it was that it was half-game and half-story.

Maida's Little Shop |Inez Haynes Irwin
We slept in a half-story room with windows opening on the porch roof.

South American Fights and Fighters |Cyrus Townsend Brady

Lena climbed to her room in the third half-story of the Quarrymen's Hotel.

Heart of the West |O. Henry