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We have determined spectroscopic orbits for three chromsopherically active giants that have hot compact companions. They are HD 160538 (KO III + wd, P = 904 days), HD 165141 (G8 III + wd, P approximately 5200 days), and HD 185510 (KO III + sdB, P = 20.6619 days). By fitting an IUE spectrum with theoretical models, we find the white dwarf companion of HD 165141 has a temperature of about 35,000 K. Spectral types and rotational velocities have been determined for the three giants and distances have been estimated. These three systems and 39 Ceti are compared with the barium star mass-transfer scenario. The long-period mild barium giant HD 165141 as well as HD 185510 and 39 Ceti, which have relatively short periods and normal abundance giants, appear to be consistent with this scenario. The last binary, HD 160538, a system with apparently near solar abundances, a white dwarf companion, and orbital characteristics similar to many barium stars, demonstrates that the existence of a white dwarf companion is insufficient to produce a barium star. The paucity of systems with confirmed white dwarf companions makes abundance analyses of HD 160538 and HD 165141 of great value in examining the role of metallicity in barium star formation.