  Electroweak precision data have been extensively used to constrain models
containing physics beyond that of the Standard Model. When the model contains
Higgs scalars in representations other than singlets or doublets, and hence rho
not equal to 1 at tree level, a correct renormalization scheme requires more
inputs than the three commonly used for the Standard Model case. In such cases,
the one loop electroweak results cannot be split into a Standard Model
contribution plus a piece which vanishes as the scale of new physics becomes
much larger than M_W. We illustrate our results by presenting the dependence of
M_W on the top quark mass in a model with a Higgs triplet and in the SU(2)_L x
SU(2)_R left-right symmetric model. In these models, the allowed range for the
lightest neutral Higgs mass can be as large as a few TeV.
