Military headgear very good? Not half, very good! (4)

I believe the answer is:

kepi

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'military headgear' is the definition.
(I've seen this in another clue)

I cannot understand how the remainder of the clue works.

Can you help me to learn more?

(Other definitions for kepi that I've seen before include "French military hat" , "French army cap" , "Flat-topped military cap" , "Military cap with circular top" , "French military headgear" .)

I've seen this clue in The Sunday Times and The Times.

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