Crossword Genius

Making small cocktail of martini, using bottled Asti at the end (13)

Ross

I believe the answer is:

miniaturising

I'm a little stuck... Click here to teach me more about this clue!

'making small' is the definition.

'cocktail of martini using bottled asti at the end' is the wordplay.
I cannot quite understand how this works, but
'at' is found in the answer.
This may be the basis of clue (or it may be nonsense).

Can you help me to learn more?

(Another definition for miniaturising that I've seen is " Making smaller".)

I've seen this clue in The Telegraph.
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