  Recently full O(alpha_s^2, alpha_s*beta, beta^2) corrections to the threshold
total cross section for e+e- to ttbar have been calculated, and the reported
corrections turned out to be unexpectedly large. We study how to reduce
theoretical uncertainties of the cross section. We adopt a new mass definition
proposed by Beneke, which incorporates a renormalon-pole cancellation in the
total energy of a static quark-antiquark pair. This improves the convergence of
the 1S resonance mass, while the normalization of the cross section scarcely
changes. We argue that resummations of logarithms are indispensable, since two
largely separated scales dictate the shape of the cross section. As a first
step, we resum logarithms in the Coulombic part of the t-tbar potential and
observe a considerable improvement in the convergence of corresponding
corrections. There still remain, however, large corrections, which arise from a
1/r^2 term in the ttbar potential. We also calculate full O(alpha_s^2,
alpha_s*beta, beta^2) corrections to the momentum distributions of top quarks
in the threshold region. Corrections to the distribution shape are small on the
1S resonance. At higher energies, corrections become larger.
