  Neutrinoless 3-prong tau lepton decays into a charged lepton and either two
charged particles or one neutral meson have been searched for using 4.79
fb^{-1} of data collected with the CLEO II detector at CESR. This analysis
represents an update of a previous study and the addition of six decay
channels. In all channels the numbers of events found are compatible with
background estimates and branching fraction upper limits are set for 28
different decay modes. These limits are either more stringent than those set
previously or represent the first attempt to find these decays.
