We present preliminary results from HI observations of a new sample of compact groups done with the Parkes telescope, as well as from images made with the Australia Telescope Compact Array (ATCA). These observations confirm earlier claims that a significant fraction of compact groups are deficient in HI, and hence that a significant fraction of groups of galaxies that appear compact on the sky are indeed compact systems. The ATCA observations of a very HI-poor group suggest that this group is a true compact system in an advanced stage of evolution. However, the ATCA observations also show that HI-rich groups exist that are genuinely compact.