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1.
A criticism or insult disguised as a compliment.

A compliment with two meanings, one of which is unflattering to the receiver.

Also called backhanded compliment
Patti sees Britney wearing a sexy new dress. Patti, who really doesn't like Britney, says, "That dress is really sharp. It really makes you look so slim!" Left handed compliment: "You're fat, and that dress makes you look like you're trying to hide it."

"Boy, you're pretty hot... for a fat (or skinny) chick!" Left handed compliment: Self-explanatory
by For Whom the Bell Trolls June 08, 2006
 
2.
An insult disguised as a compliment.
A left handed compliment would be something like the following..."I like your imperfections. Without them you'd be really hot, but boring."
by NLM1992 July 02, 2009