  We consider top-anti-top production near threshold in $e^+ e^-$ collisions,
resumming Coulomb-enhanced corrections at next-to-next-to-leading order (NNLO).
We also sum potentially large logarithms of the small top quark velocity at the
next-to-leading logarithmic level using the renormalization group. The NNLO
correction to the cross section is large, and it leads to a significant
modification of the peak position and normalization. We demonstrate that an
accurate top quark mass determination is feasible if one abandons the
conventional pole mass scheme and if one uses a subtracted potential and the
corresponding mass definition. Significant uncertainties in the normalization
of the $t\bar{t}$ cross section, however, remain.
