  We compare phenomenological values of the frozen QCD running coupling
constant ($\alpha_s$) with two classes of solutions obtained through
nonperturbative Schwinger-Dyson equations. We use these same solutions with
frozen coupling constants as well as their respective nonperturbative gluon
propagators to compute the QCD prediction for the asymptotic pion form factor.
Agreement between theory and experiment on $\alpha_s(0)$ and $F_\pi (Q^2)$ is
found only for one of the solutions Schwinger-Dyson equations.
