Not so high praise (7)

I believe the answer is:

flatter

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'praise' is the definition.
(flattering is a kind of praising)

I can't explain the remainder of the clue.

(Other definitions for flatter that I've seen before include "sugar" , "Comparatively deflated" , "Compliment dishonestly" , "resort to cajolery" , "more lifeless" .)

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

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