Carefully change great song (4-4)

I believe the answer is:

fine-tune

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

'carefully change great song' is the definition.
I can't judge whether this defines the answer.

'great song' is the wordplay.
'great' becomes 'fine' (fine can mean great in phrases like fine art).
'song' becomes 'tune' (I've seen this before).
'fine'+'tune'='FINE-TUNE'

Can you help me to learn more?

(Other definitions for fine-tune that I've seen before include "Improve, making small adjustments" , "Make small adjustments (to)" .)

I've seen this clue in the Sydney Morning Herald.

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