Stable perturbative QCD predictions at moderate energies with a modified couplant

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.