As part of our programme to map the large-scale distribution of galaxies behind the southern Milky Way, we observed 314 optically-selected, partially-obscured galaxies in the Zone of Avoidance (ZOA) in the Crux and Great Attractor (GA) regions. An additional 29 galaxies were observed in the Vela ZOA survey region (because of the small numbers they are not discussed any further). The observations were conducted with the Parkes 64m (210 ft) radio telescope, in a single-pixel pointed mode, reaching an rms noise level of typically 2-6mJy over the velocity search range of 400