More on Neat as a Bandbox from Infoplease:

• Neat as a Bandbox - Neat as a Bandbox A band-box is a slight box for caps, hats, and other similar articles. Source: ...
• Bandbox - Bandbox He comes out of a bandbox—i.e. he is so neat and precise, so carefully got up in his ...
• Dictionary of Phrase and Fable: N - Definitions, origins, and illustrative excerpts for words, phases, and literary allusions starting with "N"