  We calculate the O($\alpha_s$) gluon Bremsstrahlung corrections to the
inclusive decay $b \rightarrow s \gamma$, involving the full operator basis
$\hat O_1$ -- $\hat O_8$. Confirming and extending earlier calculations of Ali
and Greub, we give formulas for the total decay width as well as the
perturbative photon spectrum, regarding the former as a necessary part of the
forthcoming complete NLO analysis. We explore in detail the renormalization
scale dependence of our results and find it considerably increased.
