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Radial velocities from the 2.1 m telescope at McDonald Observatory and the coudé feed telescope at Kitt Peak National Observatory are used to determine new spectroscopic orbits for the double-lined spectroscopic binaries HR 2962 (F5V), HD 214686 (F8IV), and 16 Psc (F6Vb vw). The new orbital dimensions (a1sin i and a2sin i) and minimum masses (m1sin3i and m2sin3i) have accuracies of 0.1–1%. In the case of HD 214686, which has components of nearly the same mass (m1/m2 = 1.0080 ± 0.0013), we confirm that the component labeled as the primary in previous spectroscopic studies of this system is the slightly more massive component. We find that in HR 2962 the primary is rotating much more rapidly than the pseudosynchronous rate, while the rotation of the secondary is slightly faster than pseudosynchronous; in HD 214686 the primary is rotating at the pseudosynchronous rate or perhaps slightly less, while the rotation of the secondary is pseudosynchronous; and in 16 Psc both components rotate somewhat more rapidly than the pseudosynchronous rates. The three systems, which are of naked-eye brightness, are good potential targets for resolution by modern optical interferometers and so are promising candidates for full determination of their orbits and associated precise masses and distances.