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We have determined improved spectroscopic orbits for three double-lined binaries, HD 82191 (Am), ω Dra (F5 V), and 108 Her (Am), 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 5.28 to 9.01 days, and all three systems have circular 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. Our improved results confirm the large minimum masses of HD 82191 and also agree with the values previously found for ω Dra. However, for the components of 108 Her our minimum masses are about 20% larger than the previous best values. We conclude that both components of HD 82191 as well as the primary of 108 Her are Am stars. However, the A9 secondary of 108 Her has normal abundances. We estimate spectral types of F4 dwarf and G0 dwarf for the components of ω Dra. The primaries of the three binaries are synchronously rotating as is the secondary of 108 Her. The secondaries of HD 82191 and ω Dra are possibly synchronously rotating.