  We present a calculation of the branching ratio $\brbsg$ in two well
motivated supersymmetric models: the minimal $SU(5)$ and the no-scale flipped
$SU(5)$ supergravity models. We find that the improved CLEO upper bound
($\brbsg<5.4\times10^{-4}$ at 95\% CL) does not yet constrain the minimal
$SU(5)$ supergravity model, where $\brbsg_{minimal}=(2.3-3.6)\times10^{-4}$. In
the flipped $SU(5)$ model the CLEO bound is constraining, although still not
very significantly, even for light charged Higgs masses. An improvement in
sensitivity by a factor of two will probe all (more than half) of the parameter
space of the minimal (flipped) $SU(5)$ supergravity model. This ``resolution"
of the $\bsg$ microscope far surpasses that of present collider experiments. In
the flipped model there exists a significant region of parameter space where
$\brbsg$ is highly suppressed due to a new phenomenon involving a complicated
cancellation against the QCD correction parameter.
