The occurrence of fixed points in the renormalization group evolution
of R-parity-violating (RPV) couplings in the minimum supersymmetric st
andard model (MSSM) is quantified, assuming that third generation coup
lings are dominant. These fixed points give new upper bounds on the RP
V couplings at the electroweak scale. To avoid unacceptable top-quark
decays the final-state sparticles participating in these RPV decays mu
st have masses greater than or similar to m(t). We also discuss possib
le RPV signals at the upgraded LEP collider from pair production and d
ecay of the lightest sparticle (expected to be the lightest neutralino
but possibly a sneutrino).