While making radial-velocity observations of stars in the declination range 0° ^ 8 ^ -30° which had no previously reported velocity, we discovered a number of variable velocity objects. Reported here are the orbital analyses of the first three stars from this group: HR 1120, HR 7038, and HR 7617. HR 7038 has an F5 V primary and is found to have a highly eccentric orbit. HR 1120 and HR 7617 are both late-type giant stars with orbital periods less than 100 days. In all three systems, we suspect that the secondary is a normal main-sequence star.