We present new redshifts of ten rich clusters of galaxies of the Abell, Corwin, and Olowin cluster catalog (Abell's southern extension). These are the first results of a survey of southern cluster redshifts which we intend to complete out to z~0.1. In six clusters we measured the redshifts of the first and second brightest galaxy, obtaining typical differences of ~650 km s^-1^. This gives confidence in both the identification of the brightest galaxies and the redshift measurement. We also found that the redshifts we obtained agree well with the log (cz)-m_10_ relationship.