We have conducted a search of 19 southern Galactic globular clusters for su
bmillisecond pulsars at 660 MHz with the Parkes 64 m radio telescope. To mi
nimize dispersion smearing we used the CPSR baseband recorder, which sample
s the 20 MHz observing band at the Nyquist rate. By possessing a complete d
escription of the signal we could synthesize an optimal filter bank in soft
ware, and in the case of globular clusters of known dispersion measure, muc
h of the dispersion could be removed using coherent techniques. This allowe
d for very high time resolution (25.6 ks in most cases), making our searche
s in general sensitive to submillisecond pulsars with flux densities greate
r than about 3 mJy at 50 cm. No new pulsars were discovered, placing import
ant constraints on the proportion of pulsars with very short spin periods i
n these clusters.