  Combining recent perturbative analyses on the static QCD potential and the
quark pole mass, we find that, for the heavy quarkonium states $c\bar{c}$,
$b\bar{b}$ and $t\bar{t}$, (1) ultra-soft (US) corrections in the binding
energies are small, and (2) there is a stronger cancellation of IR
contributions than what has been predicted by renormalon dominance hypothesis.
By contrast, for a hypothetical heavy quarkonium system with a small number of
active quark flavors ($n_l\approx 0$), we observe evidence that renormalon
dominance holds accurately and that non-negligible contributions from US
corrections exist. In addition, we examine contributions of renormalons at $u=-
1$. As an important consequence, we improve on a previous prediction for
possible achievable accuracy of top quark $\overline{\rm MS}$--mass measurement
at a future linear collider and estimate that in principle 20--30~MeV accuracy
is reachable.
