  The CKM matrix element $|V_{cb}|$ can be extracted by combining data from
experiments with lattice QCD results for the semileptonic form factors for the
$\bar{B}\to D^{(*)} \ell \bar{\nu}$ decays. The Oktay-Kronfeld (OK) action was
designed to reduce heavy-quark discretization errors to below $1\%$, or through
$\mathcal{O}(\lambda^3)$ in HQET power counting. Here we describe recent
progress on bottom-to-charm currents improved to the same order in HQET as the
OK action, and correct formerly reported results of our matching calculations,
in which the operator basis was incomplete.
