  The evaluation of high-energy cross sections involving the SM Higgs boson
requires the use of the Higgs running coupling $\lambda(\mu)$. Taking $\mu$ to
be equal to the center-of-mass energy $\sqrt{s}$ of the scattering process, the
perturbative approach fails for relatively small values of the Higgs mass and
coupling, $\lambda(\sqrt{s})\approx 2.2$. Performing an approximate resummation
of ``bubble'' Feynman diagrams, we find the scale $\mu=\sqrt{s}/ e \approx
\sqrt{s}/2.7$ to yield reliable perturbative results, even for large Higgs mass
and coupling. The new perturbative upper limit on the Higgs running coupling is
$\lambda(\sqrt{s}/ e)\approx 4$.
