  We report on a deep radio search for a pulsar wind nebula associated with the
radio-quiet neutron star RX J0822-4300 in the supernova remnant Puppis A. The
well-determined properties of Puppis A allow us to constrain the size of any
nebula to less than 30 arcsec; however we find no evidence for such a source on
any spatial scale up to 30 arcmin. These non-detections result in an upper
limit on the radio luminosity of any pulsar-powered nebula which is three
orders of magnitude below what would be expected if RX J0822-4300 was an
energetic young radio pulsar beaming away from us, and cast doubt on a recent
claim of X-ray pulsations from this source. The lack of a radio nebula leads us
to conclude that RX J0822-4300 has properties very different from most young
radio pulsars, and that it represents a distinct population which may be as
numerous, or even more so, than radio pulsars.
