Speak softly by small dog's cage (4,2)

I believe the answer is:

coop up

'cage' is the definition.
(thesaurus)

'speak softly by small dog's' is the wordplay.
'speak softly' becomes 'coo' (cooing is a kind of speaking softly).
'by' is a charade indicator (letters next to each other).
'small dog' becomes 'pup' (I've seen this before).
'coo'+'pup'='COOP UP'

(Another definition for coop up that I've seen is " Confine".)

I've seen this clue in The Times.

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