  We introduce a new sum-rule for large-$N_c$ QCD which relates the density of
heavy quarkonium states, the state-averaged square of the wavefunction at the
origin, and the heavy quark current-current correlator. Focusing on the region
of energy just above perturbative threshold, we calculate the correlator by
incorporating arbitrarily high orders in the QCD coupling $\alpha_s$. We use
the sum-rule to determine the bottomonium potential using experimentally
measured s-wave leptonic widths and compare the result with the potential
obtained by direct calculation from the measured s-wave spectrum. We discuss
the utility of the sum-rule method for accurate determination of the confining
potential.
