Shut tight (5)

I believe the answer is:

This clue is a double definition.

'shut' is the first definition.
(I know that shut can be written as close)

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

(Other definitions for close that I've seen before include "Heavy" , "Near - conclusion" , "Cathedral's precincts" , "Dense; nearby" , "residential street" .)

I've seen this clue in The Globe and Mail and The Irish News.

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