  We re-evaluate the non-perturbative contribution to the thrust distribution
in $e^+e^-\to$ hadrons, in the light of the latest experimental data and the
recent NNLO perturbative calculation of this quantity. By extending the
calculation to NNLO+NLL accuracy, we perform the most detailed study to date of
the effects of non-perturbative physics on this observable. In particular, we
investigate how well a model based on a low-scale QCD effective coupling can
account for such effects. We find that the difference between the improved
perturbative distribution and the experimental data is consistent with a
$1/Q$-dependent non-perturbative shift in the distribution, as predicted by the
effective coupling model. Best fit values of $\alpha_s(M_Z) =
0.1164^{+0.0028}_{-0.0026}$ and $\alpha_0(2 GeV)=0.59+/-0.03$ are obtained with
$\chi^2/d.o.f.=1.09$. This is consistent with NLO+NLL results but the quality
of fit is improved. The agreement in $\alpha_0$ is non-trivial because a part
of the 1/Q-dependent contribution (the infrared renormalon) is included in the
NNLO perturbative correction.
