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

I believe the answer is:
enhancement
'improvement' is the definition.
(enhancement is a kind of improvement)
'working the middle of dennis the menace' is the wordplay.
'working' indicates an anagram.
'middle of' indicates the central letters.
The central letters of 'dennis' are 'nn'.
'the'+'nn'+'menace'='thennmenace'
'thennmenace' with letters rearranged gives 'ENHANCEMENT'.
'seen by re' acts as a link.
I am not very happy about this link. Some or all of it may be part of another bit of the clue.
Can you help me to learn more?
(Other definitions for enhancement that I've seen before include "this will improve things" , "Improvement in quality" , "What improves" , "Improving change" , "Heightening" .)
