Wet blanket wraps many tight (7)

I believe the answer is:

miserly

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'tight' is the definition.
(I know that tight can be written as miserly)

I cannot understand how the remainder of the clue works.

(Other definitions for miserly that I've seen before include "Mean with money" , "Penny-pinching" , "Paltry" , "Like Scrooge" , "Mean, tight" .)

I've seen this clue in The Daily Express.

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