  We perform numerical analysis of double-pinched Borel-Laplace QCD sum rules
for the strangeless semihadronic $\tau$-decay data. The $D=0$ contribution to
the theoretical contour integral in the sum rules is evaluated by the
(truncated) Fixed Order perturbation theory method (FO) and by the Principal
Value (PV) of the Borel integration. We use for the full Adler function the
Operator Product Expansion (OPE) with the terms $\sim \langle O_D \rangle$ of
dimension $D=2 n$ where $2 \leq n \leq 5$ for the (V+A)-channel, and $2 \leq n
\leq 7$ for the V-channel data. In our previous works [1,2], only the
(V+A)-channel data was analysed. In this work, the analysis of a new set of
V-channel data is performed as well. Further, a renormalon-motivated
construction of the $D=0$ part of the Adler function is improved in the $u=3$
infrared renormalon sector, by involving the recently known information on the
two principal noninteger values $k^{(j)}=\gamma^{(1)}(O_6^{(j)})/\beta_0$ of
the effective leading-order anomalous dimensions. Additionally, the OPE of the
Adler function has now the D=6 contribution with the principal anomalous
dimension ($\sim \alpha_s^{k^{(1)}}$), and terms of higher dimension (with zero
anomalous dimension). Cross-checks of the obtained extracted values of
$\alpha_s$ and of the condensates were performed by reproduction of the
(central) experimental values of several double-pinched momenta $a^{(2,n)}$.
The averaged final extracted values of the (MSbar) coupling are:
$\alpha_s(m_{\tau}^2) = 0.3169^{+0.0070}_{-0.0096}$, corresponding to
$\alpha_s(M_Z^2)=0.1183^{+0.0009}_{-0.0012}$.
