We report the results of a survey of the Small Magellanic Cloud (SMC) for r
adio pulsars conducted with the 20 cm multibeam receiver of the Parkes 64 m
telescope. This survey targeted a more complete region of the SMC than a p
revious pulsar search and had an improvement in sensitivity by a factor of
about 2 for most pulsar periods. This survey is much more sensitive to fast
young pulsars (with P less than or similar to 100 ms) and is the first sur
vey of the SMC with any sensitivity to millisecond pulsars. Two new pulsars
were discovered in the survey, one of which is located within the SMC. The
number of pulsars found in the survey is consistent with the expected numb
er derived using several methods. We also report the serendipitous discover
y of a new pulsar in the 30 Doradus region of the Large Magellanic Cloud (L
MC). These discoveries bring the total number of rotation-powered pulsars c
urrently known in the Magellanic Clouds to eight. We have also made refined
timing measurements for the new discoveries as well as for three previousl
y known LMC pulsars. The age distribution of luminous Magellanic Cloud puls
ars supports the conjecture that pulsars younger than about 5 Myr are more
luminous on average than older pulsars.