A compliment with two meanings, one of which is unflattering to the receiver: “The senator said that her opponent was quite competent for someone so inexperienced; you hear nothing but left-handed compliments in these debates.”
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Words nearby left-handed compliment
Idioms and Phrases with left-handed compliment
Also, backhanded compliment. An insult in the guise of an expression of praise. For example, She said she liked my hair, but it turned out to be a left-handed compliment when she asked how long I'd been dyeing it. This expression uses left-handed in the sense of “questionable or doubtful,” a usage dating from about 1600.