  Previous work has suggested that perturbation theory is unreliable for Higgs-
and Goldstone-boson scattering, at energies above the Higgs mass, for
relatively small values of the Higgs quartic coupling $\lambda(\mu)$. By
performing a summation of nonlogarithmic terms, we show that perturbation
theory is in fact reliable up to relatively large coupling. This eliminates the
possibility of a strongly-interacting standard Higgs model at energies above
the Higgs mass, complementing earlier studies which excluded strong
interactions at energies near the Higgs mass. The summation can be formulated
in terms of an appropriate scale in the running coupling,
$\mu=\sqrt{s}/e\approx\sqrt{s}/2.7$, so it can easily be incorporated in
renormalization-group improved tree-level amplitudes as well as higher-order
calculations.
