Crush hat

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a hat which collapses, and can be carried under the arm, and when expanded is held in shape by springs; hence, any hat not injured by compressing.

See also: Crush

Webster's Revised Unabridged Dictionary, published 1913 by G. & C. Merriam Co.
References in periodicals archive ?
The winners also get Blue Crush on DVD, a Blue Crush hat, Blue Crush T-shirt and ring/bracelet sets.
Glenn Fleshler's Yepikhodov, the absurdly clumsy clerk, manages to crush hat boxes and stumble over what little furniture there is with a cautiously controlled sense of slapstick.