  Within an effective field theory framework, we obtain an expression, with
O(1/m^2) accuracy, for the energies of the gluonic excitations between heavy
quarks, which holds beyond perturbation theory. For the singlet heavy
quark--antiquark energy, in particular, we also obtain an expression in terms
of Wilson loops. This provides, twenty years after the seminal work of Eichten
and Feinberg, the first complete expression for the heavy quarkonium potential
up to O(1/m^2) for pure gluodynamics. Several errors present in the previous
literature (also in the work of Eichten and Feinberg) have been corrected. We
also briefly discuss the power counting of NRQCD in the non-perturbative
regime.
