  We compute the complete leading-log terms of the
next-to-next-to-next-to-leading-order corrections to potential NRQCD. As a
by-product we obtain the leading logs at $O(m\alpha_s^5)$ in the heavy
quarkonium spectrum. These leading logs, when $\Lambda_{QCD} \ll m\alpha_s^2$,
give the complete $O(m\alpha_s^5 \ln \alpha_s)$ corrections to the heavy
quarkonium spectrum.
