  We present an updated version of a QCD coupling which fulfills various
physically motivated conditions: at high momenta it practically coincides with
the perturbative QCD (pQCD) coupling; at intermediate momenta it reproduces
correctly the physics of the semihadronic tau decay; and at very low momenta it
is suppressed as suggested by large-volume lattice calculations. An earlier
presented analysis is updated here in the sense that the Adler function, in the
regime $|Q^2| \lesssim 1 \ {\rm GeV}^2$, is evaluated by a renormalon-motivated
resummation method. This Adler function is then used here in the evaluation of
the quantities related with the semihadronic (strangeless) $\tau$-decay
spectral functions, including Borel-Laplace sum rules in the (V+A)-channel. The
analysis is then extended to the evaluation of the hadronic vacuum polarization
contribution to the muon anomalous magnetic moment, $a_{\mu}^{\rm had(1)}$,
where we include in the Adler function the V-channel higher-twist OPE terms
which are regulated in the infrared (IR) by mass parameters which are expected
to be $\lesssim 1$ GeV. The correct value of $a_{\mu}^{\rm had(1)}$ can be
reproduced with the mentioned IR-regulating mass parameters if the value of the
condensate $\langle O_4 \rangle_{\rm V+A}$ is positive (and thus the gluon
condensate value is positive). This restriction and the requirement of the
acceptable quality of the fits to the various mentioned sum rules then lead us
to the restriction $0.1171 < \alpha_s(M_Z^2;{\overline{MS}}) < 0.1180$.
