Crossword Genius

What a pigeon calls parking? (4)

Ross

I believe the answer is:

coop

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'what a pigeon' is the definition.
I can't judge whether this defines the answer.

'calls parking?' is the wordplay.
'calls' becomes 'coo' (I can't justify this - if you can you should give a lot more credence to this answer).
'parking?' becomes 'p' (abbreviation on road signs).
'coo'+'p'='COOP'

Can you help me to learn more?

(Other definitions for coop that I've seen before include "Cage for poultry" , "Hens in this" , "Store" , "pound" , "Pen" .)

I've seen this clue in The Independent.
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