  We point out that applying the photon energy cut significantly modifies the
moments of energy spectrum in B->X_s+gamma decays, with a certain class of
effects not accounted for in the mostly used OPE expressions. This leads to a
systematic bias in the extracted values of the b quark mass and other heavy
quark parameters. The apparent b quark mass increases typically by 70MeV or
more, together with an even more dramatic downward shift in the kinetic
expectation value. Accounting for these cut-related shifts brings different
measurements into a good agreement, when the OPE-based theory employs the
robust approach. These nonperturbative effects are exponential in the effective
hardness severely lowered by high cuts, and do not signify a breakdown of the
1/m_b expansion itself. Similar effects in semileptonic b->c decays are briefly
addressed. We stress the utility of the second moment of E_gamma once these
effects are incorporated.
