Crossword Genius

Almost overflow (4)

Ross

I believe the answer is:

brim

'almost overflow' is the definition.
(I've seen this in another clue)

This is all the clue.

(Other definitions for brim that I've seen before include "Edge around a hat" , "Upper edge" , "Edge (of cup or hat)" , "The edge of a cup or glass" , "Lip of bowl, cup etc" .)

I've seen this clue in the LA Times.
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