  General arguments related to ``triviality'' predict that, in the broken phase
of $(\lambda\Phi^4)_4$ theory, the condensate $<\Phi>$ re-scales by a factor
$Z_{\phi}$ different from the conventional wavefunction-renormalization factor,
$Z_{prop}$. Using a lattice simulation in the Ising limit we measure
$Z_{\phi}=m^2 \chi$ from the physical mass and susceptibility and $Z_{prop}$
from the residue of the shifted-field propagator. We find that the two $Z$'s
differ, with the difference increasing rapidly as the continuum limit is
approached. Since $Z_{\phi}$ affects the relation of $<\Phi>$ to the Fermi
constant it can sizeably affect the present bounds on the Higgs mass.
