  Double-pinched Borel-Laplace sum rules are applied to ALEPH $\tau$-decay
data. For the leading-twist ($D=0$) Adler function a renormalon-motivated
extension is used, and the 5-loop coefficient is taken to be $d_4=275 \pm 63$.
Two $D=6$ terms appear in the truncated OPE ($D \leq 6$) to enable cancellation
of the corresponding renormalon ambiguities. Two variants of the fixed order
perturbation theory, and the inverse Borel transform, are applied to the
evaluation of the $D=0$ contribution. Truncation index $N_t$ is fixed by the
requirement of local insensitivity of the momenta $a^{(2,0)}$ and $a^{(2,1)}$
under variation of $N_t$. The averaged value of the coupling obtained is
$\alpha_s(m_{\tau}^2)=0.3235^{+0.0138}_{-0.0126}$ [$\alpha_s(M_Z^2)=0.1191 \pm
0.0016$]. The theoretical uncertainties are significantly larger than the
experimental ones.
