  We discuss whether or not "freezing" of the QCD running coupling constant in
the infrared region is consistent with the Schwinger -- Dyson (SD) equations.
Since the consistency of the "freezing" was not found, the conclusion is made
that the "analytization" method does not catch an essential part of
nonperturbative contributions. Proceeding from the results on consistency of
the infrared enhanced behaviour of the gluon propagator with SD equations, the
running coupling constant is modified taking into account the minimality
principle for the nonperturbative contributions in the ultraviolet region and
convergence condition for the gluon condensate. It is shown that the
requirements of asymptotic freedom, analyticity, confinement and the value of
the gluon condensate are compatible in the framework of our approach.
Possibilities to find an agreement of the enhanced behaviour of the running
coupling constant with integral estimations in the infrared region are also
discussed.
