Crossword Genius

Disagreeable nasty way out! (3)

Ross

I believe the answer is:

nay

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'disagreeable nasty way out' is the definition.
Both the definition and answer are adverbs. Perhaps they are linked in a way I don't understand?

'nasty way out' is the wordplay.
'way' becomes 'st' (abbreviation for street).
'out' indicates named letters should be taken away.
'nasty' with 'st' taken out is 'NAY'.

Can you help me to learn more?

(Other definitions for nay that I've seen before include "Negative response" , "even" , "Refusal" , "Indeed" , "Negative answer" .)

I've seen this clue in the Evening Standard.
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