  We present a specific class of models for an infrared-finite analytic QCD
coupling, such that at large space-like energy scales the coupling differs from
the perturbative one by less than any inverse power of the energy scale. This
condition is motivated by the ITEP Operator Product Expansion philosophy.
Allowed by the ambiguity in the analytization of the perturbative coupling, the
proposed class of couplings has three parameters. In the intermediate energy
region, the proposed coupling has low loop-level and renormalization scheme
dependence. The present modification of perturbative QCD must be considered as
a phenomenological attempt, with the aim of enlarging the applicability range
of the theory of the strong interactions at low energies.
