Word Study
bandbox
CIDE DICTIONARY
bandbox, n.
A light box of pasteboard or thin wood, usually cylindrical, for holding ruffs (the bands of the 17th century), collars, caps, bonnets, etc. [1913 Webster]
OXFORD DICTIONARY
bandbox, n. a usu. circular cardboard box for carrying hats.
Idiom
out of a bandbox extremely neat.
Etymology
BAND(1) + BOX(1)
For further exploring for "bandbox" in Webster Dictionary Online