Neutrinoless 3-prong tau lepton decays into a charged lepton and either two charged particles or one neutral meson have been searched for using 4.79fb^(-1) of data collected with the CLEO II detector at Cornell Electron Storage Ring. 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
