  Motivated by the recent investigation of neutrinoless $\tau$-lepton decays by
the CLEO collaboration, we perform a systematic analysis of such decays in a
possible new-physics scenario with heavy Dirac/Majorana neutrinos, including
heavy-neutrino nondecoupling effects, finite quark masses, and quark as well as
meson mixings. We find that $\tau$-lepton decays into an electron or muon and a
pseudoscalar or vector meson can have branching ratios close to the
experimental sensitivity. Numerical estimates show that the predominant decay
modes of this kind are $\tau^-\to e^-\phi$, $\tau^-\to e^-\rho^0$, and
$\tau^-\to e^-\pi^0$, with branching ratios of order $10^{-6}$.
