  Numerical simulations are performed on different lattice sizes of chiral U(1)
and SU(2) scalar-fermion models with explicit mirror pairs of fermions in the
broken symmetry phase. Relevance of these models to the electroweak theory is
discussed. Shift symmetry of the action is exploited to decouple the unwanted
mirror-fermion. Upper and lower bounds on the renormalized scalar mass as a
function of the renormalized fermion mass are obtained in the SU(2) version of
the model. Our numerical data are found to be in qualitative agreement with
one-loop results. No evidence for a nontrivial fixed point has been observed.
The mirror-fermion models are likely to be trivial in the continuum limit. Our
Monte Carlo data show that with a $180\, GeV$ top quark, the Standard Model
Higgs boson should have a mass between $100$ and $800\, GeV$.
