  The problem of precise evaluation of perturbative QCD predictions at moderate
energies is addressed. In order to improve stability of the predictions with
respect to change of the renormalization scheme it is proposed to replace the
sequence of conventional renormalization group improved approximants by a
sequence of modified approximants, involving a modified running coupling
constant, which is free from Landau singularity and much less renormalization
scheme depenedent than the conventional running coupling constant. A concrete
model of the modified coupling constant is proposed and it is shown, that the
QCD corrections to the static interquark potential evaluated with this coupling
constant are indeed much less sensitive to the scheme parameters. It is pointed
out, that the modified predictions display somewhat weaker energy dependence
compared to the conventional predictions, which may help accomodate in a
consistent way some very low and very high energy determinations of the strong
coupling constant.
