  Mixing between light and heavy neutrino states has been proposed as an
explanation (or partial explanation) for the 3-sigma NuTeV anomaly and the
2-sigma departure of the $Z^0$ invisible width from its expected value. I
assume herein that neutrino masses and mixings result from the conventional
seesaw mechanism involving six chiral neutrino states, the first three being
members of weak doublets, the others weak singlets. A finely-tuned choice of
both the (bare) Majorana masses and the (Higgs-induced) Dirac masses can fit
solar and atmospheric neutrino data and also result in significant (but
necessarily flavor-dependent) mixing between singlet and doublet states such as
would yield detectable suppression of light neutrino interaction amplitudes.
The possibility for this kind of suppressive mixing is constrained by the
observed upper limit on radiative muon decay.
