To fasten with a cinch…. Hence, to have a man “in a tight place.”

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1875.  A man who is hurt in a mining transaction is “cinched.” [San Francisco localism.]—S. Williams, ‘The City of the Golden Gate,’ Scribner’s Mag., x. p. 277 (July). (N.E.D.)

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1878.  Saddles are carefully set, and mules “cinched” with these mountain girths, eight inches wide, until it seems they can scarcely breathe; for we are to have perils of water and mountain—perils by the way.—J. H. Beadle, ‘Western Wilds,’ p. 156.

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1878.  With all set, and everything tightly “cinched,” we took the start with guide in front.—Id., p. 152.

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