  We investigate the two main uncertainties on the extraction of the
nonperturbative matrix elements $\bar{\Lambda}$ and $\lambda_1$ from moments of
the inclusive rare FCNC decay $B \to X_s \gamma$. The first one is due to
unknown matrix elements of higher dimensional operators which are estimated by
varying the matrix elements in a range as suggested by dimensional analysis.
The effect of these terms is found to be small. A second uncertainty arises
from a cut on the photon energy and we give model independent bounds on these
uncertainties as well as their estimates from a simplified version of the ACCMM
model.
