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By operating at magic wavelengths for pairs of counter-propagating red- and blue-detuned trapping beams, differential scalar light shifts are eliminated, and vector shifts are suppressed by ~250. We thereby measure an absorption linewidth \\Gamma/2\\pi = 5.7 \\pm 0.1 MHz for the Cs 6S1/2,F=4 - 6P3/2,F'=5 transition, where \\Gamma/2\\pi = 5.2 MHz in free space. Optical depth d~66 is observed, corresponding to an optical depth per atom d_1~0.08. 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