Neutrinoless 3-prong tau lepton decays into a charged lepton and eithe
r two charged particles or one neutral meson have been searched for us
ing 4.79 fb(-1) of data collected with the CLEO II detector at Cornell
Electron Storage Ring. This analysis represents an update of a previo
us study and the addition of six decay channels. In all channels the n
umbers of events found are compatible with background estimates and br
anching fraction upper limits are set for 28 different decay modes. Th
ese limits an either more stringent than those set previously or repre
sent the first attempt to find these decays.