To set to rights; to clean up. The N.E.D. furnishes 16th c. Scottish examples. The word came into the U.S. by means of settlers from Scotland.

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1842.  I never used to red up their chamber without thinking of it.—Phila. Spirit of the Times, Aug. 12.

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1896.  “You got your front room red up, Emarine?” “No; I ain’t had time to red up anything.”—Ella Higginson, ‘Tales from Puget Sound,’ p. 132.

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