  We consider a hypothetical scenario in which the Higgs boson is absent, and
attempt to constrain the mass scale Lambda of the new physics that would take
its place. Using recent measurements of sin^2(theta_eff^lept) and M_W, we show
that, in a class of theories characterized by simple conditions, the upper
bound on Lambda is close to or smaller than the SM upper bound on M_H, while in
the complementary class Lambda is not restricted by our considerations. The
issue of fine-tuning when Lambda is large is briefly discussed. As a by-product
of our considerations, we discuss the usefulness and important properties of a
radiative correction, Delta r_eff, that directly links sin^2(theta_eff^lept)
with alpha, G_mu, and M_Z.
