Radial Velocities of Bright Southern Stars is the result of an effort to determine radial velocities for those southern stars in the "Bright Star Catalogue" with no previously published radial velocity. This version of the catalog combines three lists of data published separately during 1983-85, the first for B-type stars, the second for late-type stars, and the last for A- and F-type stars. J. Andersen notes the following in a 1987 private communication: "In order to make the 1982 edition of the 'Bright Star Catalogue' as complete as possible, preliminary or even incomplete data for many stars in this catalogue were provided in advance of publication. The present catalogue presents the final values, which should supersede (not be averaged with!) those given in the Bright Star Catalogue." The method employed throughout the entire observation program is described by Andersen & Nordstroem (1983A&A...122...23A).