  We re-examine the possible magnitude of the supersymmetric contribution to
$R_b\equiv\Gamma(Z^0\to\bar b b)/\Gamma(Z^0\to{\rm all})$ in the light of the
constraints imposed by the absence of light charginos at LEP~1.5, implementing
also other available phenomenological constraints. We find the supersymmetric
contribution to be $R^{\rm susy}_b < 0.0017$, and discuss the extent to which
this upper bound could be strengthened by future constraints on the chargino
and top-squark masses. Such values of $R^{\rm susy}_b$ tend to disfavor a
supersymmetry explanation of the apparent $R_b$ discrepancy.
