  We calculate, in the framework of QCD sum rules and to next-to-leading order
in perturbation theory, the universal function $\xi_3(v\cdot v')$ which appears
at order $1/m_Q$ in the heavy quark expansion of meson weak decay form factors.
We find that radiative corrections of order $\alpha_s$ are very important. Over
the kinematic range accessible in semileptonic decays, $\xi_3(v\cdot v')$ is
proportional to the leading-order Isgur-Wise function $\xi(v\cdot v')$ to very
good accuracy. Taking into account all sources of uncertainty, we estimate
$\xi_3/\xi=(0.6\pm 0.2)$. This reduces the theoretical uncertainty in the
extraction of $|\,V_{cb}|$ from $\bar B\to D\,\ell\, \bar\nu$ transitions. A
measurement of the form factor ratio $A_2/A_1$ in $\bar B\to D^*\ell\,\bar\nu$
decays can be used to test our prediction.
