Doubly small for a defender (7)

I believe the answer is:

sweeper

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'defender' is the definition.
(I know that sweeper is a type of centre-back)

'doubly small for a' is the wordplay.
'doubly small for' becomes 'swee' (I can't explain this - if you can you should give a lot more credence to this answer).
'a' becomes 'per' (eg 'one a day' means 'one per day').
'swee'+'per'='SWEEPER'

Can you help me to learn more?

(Other definitions for sweeper that I've seen before include "Last football defender before the goalkeeper" , "'Football defender, carries a brush (7)'" , "Soccer player" , "Soccer defender" , "Back" .)

I've seen this clue in The Guardian.

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