  The problem of precise evaluation of the perturbative QCD predictions at
moderate energies is considered. Substantial renormalization scheme dependence
of the perturbative predictions obtained with the conventional renormalization
group improved perturbative approximants is discussed, using as an example the
QCD effective charge appearing in the static interquark potential and the QCD
corrections to the Gross-Llewellyn-Smith sum rule in the deep inelastic
neutrino-nucleon scattering. A new method for evaluating the QCD predictions at
moderate energies is proposed, based on a modified couplant, which is
constructed to be free from Landau singularity and less renormalization scheme
dependent than the conventional couplant. The modified couplant contains an
adjustable parameter, which may be used to improve the modified perturbative
predictions in low orders by utilizing some information outside of perturbation
theory. This parameter is fixed by matching the modified predictions to the
phenomenological expression for the effective charge in the interquark
potential. The renormalization scheme dependence of the perturbative
predictions in the modified expansion is then discussed in detail, including
the predictions selected by the Principle of Minimal Sensitivity applied to the
modified expansion. It is shown that the predictions obtained in the modified
expansion are much more stable with respect to change of the renormalization
scheme parameters than the predictions obtained in the conventional approach.
It is also found that the modified predictions display somewhat weaker energy
dependence then the predictions obtained with the conventional expansion, which
may help accommodate in a consistent way some low values of the strong coupling
parameter measured at low energies with the values measured at high energies.
