  We discuss the new model expression $\bar{\alpha}_{an}(Q^2)$ recently
obtained for the QCD running coupling with a regular ghost-free behavior in the
"low $Q^2$" region. Being deduced from the standard "asymptotic-freedom"
expression by imposing the $Q^2$-analyticity -- without any adjustable
parameters -- it obeys nice features: (i) The universal limiting value
$\bar{\alpha}_{an}(0)=4\pi /\beta_0 \simeq 1.4$ expressed only via group
symmetry factors and independent of experimental estimates on the running
coupling $\bar{\alpha}_s(Q^2)$ (of QCD scale parameter $\Lambda$). This value
turns out to be stable with respect to higher order corrections; (ii) Stability
of IR behavior with respect to higher-loop effects; (iii) Coherence between the
experimental $\bar{\alpha}_{an}(M_{\tau}^2)$ value and integral information on
IR $\bar{\alpha}_s(Q^2)$ behavior as extracted from jet physics data.
