Carefully adjust enjoyable melody (4-4)
I believe the answer is:
fine-tune
'carefully adjust' is the definition.
(to fine-tune is to make small adjustments)
'enjoyable melody' is the wordplay.
'enjoyable' becomes 'fine'.
'melody' becomes 'tune' (synonyms).
'fine'+'tune'='FINE-TUNE'
(Other definitions for fine-tune that I've seen before include "Make small adjustments (to)" , "Improve, making small adjustments" .)