Peels off, not quite so disturbed (9)

I believe the answer is:

sleepless

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'quite so disturbed' is the definition.
'sleepless' can be an answer for 'disturbed' (thesaurus). I'm not certain of the 'quite so' bit.

'peels off not' is the wordplay.
'off' indicates an anagram.
'not' becomes 'less' (I've seen this in other clues).
'peels' with letters rearranged gives 'sleep'.
'sleep'+'less'='SLEEPLESS'

Can you help me to learn more?

(Other definitions for sleepless that I've seen before include "Film: '-- in Seattle'" , "Suffering from insomnia, not in the land of Nod" , "Insomniac" .)

I've seen this clue in The Daily Express.

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