  We study the inter-relations that exist between the present experimental
bounds on the Higgs mass, as obtained from radiative corrections to $m_W$, and
the effective parameters, $\alpha_i$ and $\Lambda$. We find that the SM bounds
on $m_H$, arising from a precise determination of the $m_W$ mass, can be
substantially modified by the presence of dimension-6 operators which appear in
the linear realization of the effective Lagrangian approach. A Higgs mass as
heavy as 700 GeV can be allowed for scales of new physics of the order of 1
TeV.
