  We present updated results of a numerical improvement test with heavy-meson
spectrum for the Oktay--Kronfeld (OK) action. The OK action is an extension of
the Fermilab improvement program for massive Wilson fermions including all
dimension-six and some dimension-seven bilinear terms. Improvement terms are
truncated by HQET power counting at $\mathrm{O}(\Lambda^3/m_Q^3)$ for
heavy-light systems, and by NRQCD power counting at $\mathrm{O}(v^6)$ for
quarkonium. They suffice for tree-level matching to QCD to the given order in
the power-counting schemes. To assess the improvement, we generate new data
with the OK and Fermilab action that covers both charm and bottom quark mass
regions on a MILC coarse $(a \approx 0.12~\text{fm})$ $2+1$ flavor,
asqtad-staggered ensemble. We update the analyses of the inconsistency quantity
and the hyperfine splittings for the rest and kinetic masses. With one
exception, the results clearly show that the OK action significantly reduces
heavy-quark discretization effects in the meson spectrum. The exception is the
hyperfine splitting of the heavy-light system near the $B_s$ meson mass, where
statistics are too low to draw a firm conclusion, despite promising results.
