Milliarcsecond-accurate radio positions for 22 southern hemisphere extragalactic sources are reported. These positions are derived from Mark III very long baseline interferometry observations made between 2003 February and 2003 August. The results presented here supplement an ongoing project to increase the sky density of southern hemisphere sources in order to better define the International Celestial Reference Frame and to provide additional phase-reference sources with accurate positions for use in astrophysical observations. The positions for all 22 sources are south of δ = -30° (positions for 10 of the sources are south of δ = -60°) and represent the largest group of new milliarcsecond-accurate astrometric positions for sources in this declination range since the initial definition of the International Celestial Reference Frame. The reported positions have average formal uncertainties of 0.5 mas in right ascension and 0.6 mas in declination.