  We consider the determination of $\alpha_s$ from $\tau$ hadronic decays, by
investigating the contour-improved (CI) and the fixed-order (FO)
renormalization group summations in the frame of a new perturbation expansion
of QCD, which incorporates in a systematic way the available information about
the divergent character of the series. The new expansion functions, which
replace the powers of the coupling, are defined by the analytic continuation in
the Borel complex plane, achieved through an optimal conformal mapping. Using a
physical model recently discussed by Beneke and Jamin, we show that the new
CIPT approaches the true results with great precision when the perturbative
order is increased, while the new FOPT gives a less accurate description in the
regions where the imaginary logarithms present in the expansion of the running
coupling are large. With the new expansions, the discrepancy of 0.024 in
$\alpha_s(m_\tau^2)$ between the standard CI and FO summations is reduced to
only 0.009. From the new CIPT we predict $\alpha_s(m_\tau^2)= 0.320
^{+0.011}_{-0.009}$, which practically coincides with the result of the
standard FOPT, but has a more solid theoretical basis.
