We resum the leading ultrasoft logs of the singlet and octet static QCD pot
entials within potential NRQCD. We then obtain the complete three-loop reno
rmalization group improvement of the singlet QCD static potential. The disc
repancies between the perturbative evaluation and the lattice results at sh
ort distances are slightly reduced. (C) 2000 Published by Elsevier Science
B.V.