  Precision electroweak data are generally believed to constrain the Higgs
boson mass to lie below approximately 190 GeV at 95% confidence level. The
standard Higgs model is, however, trivial and can only be an effective field
theory valid below some high energy scale characteristic of the underlying
non-trivial physics. Corrections to the custodial isospin violating parameter T
arising from interactions at this higher energy scale dramatically enlarge the
allowed range of Higgs mass. We perform a fit to precision electroweak data and
determine the region in the (m_H, Delta T) plane that is consistent with
experimental results. Overlaying the estimated size of corrections to T arising
from the underlying dynamics, we find that a Higgs mass up to 500 GeV is
allowed. We review two composite Higgs models which can realize the possibility
of a phenomenologically acceptable heavy Higgs boson. We comment on the
potential of improvements in the measurements of m_t and M_W to improve
constraints on composite Higgs models.
