Improvement seen by re-working the middle of Dennis the Menace (11)

I believe the answer is:

enhancement

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'improvement' is the definition.
(enhancement is a kind of improvement)

'working the middle of dennis the menace' is the wordplay.
'working' is an anagram indicator.
'middle of' says to take the centre.
The middle letters of 'dennis' are 'nn'.
'the'+'nn'+'menace'='thennmenace'
'thennmenace' with letters rearranged gives 'ENHANCEMENT'.

'seen by re' is the link.
This may not be right. Some or all of it may belong to another bit of the clue.

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(Other definitions for enhancement that I've seen before include "this will improve things" , "Improvement in quality" , "What improves" , "Improving change" , "Heightening" .)

I've seen this clue in The Times.

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