Sing outside frequently but reducing the strength (9)

I believe the answer is:

softening

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'reducing the strength' is the definition.
'softening' can be an answer for 'reducing' (thesaurus). I'm not sure about the 'the strength' bit.

'sing outside frequently' is the wordplay.
'outside' means one lot of letters goes inside another.
'frequently' becomes 'often' (synonyms).
'sing' placed around 'often' is 'SOFTENING'.

'but' acts as a link.

Can you help me to learn more?

(Other definitions for softening that I've seen before include "Cushioning" , "becoming more lenient" .)

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

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