A number of different classes of potentially extra-terrestrial bursts of radio emission have been observed in surveys with the Parkes 64-m radio telescope, including ‘rotating radio transients’, the ‘Lorimer burst’ and ‘perytons’. Rotating radio transients are radio pulsars which are best detectable in single-pulse searches. The Lorimer burst is a highly dispersed isolated radio burst with properties suggestive of extragalactic origin. Perytons share the frequency-swept nature of the rotating radio transients and Lorimer burst, but unlike these events appear in all 13 beams of the Parkes multibeam receiver and are probably a form of peculiar radio frequency interference. In order to constrain these and other radio source populations further, we searched the archival Parkes Multibeam Pulsar Survey data for events similar to any of these. We did not find any new rotating radio transients or bursts like the Lorimer burst. We did, however, discover four peryton-like events. Similar to the perytons, these four bursts are highly dispersed, detected in all 13 beams of the Parkes multibeam receiver, and have pulse widths between 20 and 30 ms. Unlike perytons, these bursts are not associated with atmospheric events like rain or lightning. These facts may indicate that lightning was not responsible for the peryton phenomenon. Moreover, the lack of highly dispersed celestial signals is the evidence that the Lorimer burst is unlikely to belong to a cosmological source population.