  QCD contributions to the $b \to u \ell^- \bar{\nu}_\ell$ decay rate, which
are known to two-loop order in the $\bar{MS}$ scheme, exhibit sufficient
dependence on the renormalization mass $\mu$ to compromise phenomenological
predictions for inclusive semileptonic $B \to X_u$ processes. Such scale
dependence is ameliorated by the renormalization-group (RG) extraction and
summation of all leading and RG-accessible subleading logarithms occurring
subsequent to two-loop order in the perturbative series. This optimal
RG-improvement of the known portion of the perturbative series virtually
eliminates $\mu$-dependence as a source of theoretical uncertainty in the
predicted semileptonic $B \to X_u$ inclusive rate.
