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We have determined improved spectroscopic orbits for three double-lined binaries, 66 And (F4 V), HR 6979 (Am), and HR 9059 (F5 IV) using radial velocities from the 2.1 m telescope at McDonald Observatory, the coudé feed telescope at Kitt Peak National Observatory, and 2 m telescope at Fairborn Observatory. The orbital periods range from 11.0 to 14.3 days, and all three systems have eccentric orbits. The new orbital dimensions (a1 sin i and a2 sin i) and minimum masses (m1 sin3 i and m2 sin3 i) have accuracies of 0.2% or better. All six components of the three binary systems are rotating more slowly than their predicted pseudosynchronous rotational velocities. Hipparcos photometry of HR 9059 shows that this system has partial eclipses. Its components are nearly identical in mass and are at the very end of their main-sequence lifetimes or perhaps have just begun to traverse the Hertsprung gap.