  Using results on soft-collinear factorization for inclusive B-meson decay
distributions, a systematic study of the partial B->Xs+gamma decay rate with a
cut E_gamma<E_0 on photon energy is performed. For values E_0<1.9 GeV the rate
can be calculated without reference to shape functions. The result depends on
three large scales: m_b, \sqrt{m_b Delta}, and Delta=m_b-2E_0. The sensitivity
to the scale Delta=1.1 GeV (for E_0=1.8 GeV) introduces significant
uncertainties, which have been ignored in the past. Our new prediction for the
B->Xs+gamma branching ratio with E_gamma<1.8 GeV is
Br(B->Xs+gamma)=(3.44+-0.53+-0.35)*10^{-4}, where the errors refer to
perturbative and parameter uncertainties, respectively. The implications of
larger theory uncertainties for New Physics searches are explored with the
example of the type-II two-Higgs-doublet model.
