Piece of chow, perhaps, unsmoked (3-3)

I believe the answer is:

dog-end

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'piece' is the definition.
Both the answer and definition are singular nouns.
Maybe there's a link between them I don't understand?

'chow perhaps unsmoked' is the wordplay.
'chow perhaps' becomes 'dog' (chow is a kind of dog).
'unsmoked' becomes 'end' (I can't explain this - if you can you should believe this answer much more).
'dog'+'end'='DOG-END'

'of' is the link.

Can you help me to learn more?

(Another definition for dog-end that I've seen is " Cigarette butt".)

I've seen this clue in the Evening Standard.

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