  Using the spectral functions measured in $\tau$ decays, we investigate the
actual numerical impact of duality violations on the extraction of the strong
coupling. These effects are tiny in the standard $\alpha_s(m_\tau^2)$
determinations from integrated distributions of the hadronic spectrum with
pinched weights, or from the total $\tau$ hadronic width. The pinched-weight
factors suppress very efficiently the violations of duality, making their
numerical effects negligible in comparison with the larger perturbative
uncertainties. However, combined fits of $\alpha_s$ and duality-violation
parameters, performed with non-protected weights, are subject to large
systematic errors associated with the assumed modelling of duality-violation
effects. These uncertainties have not been taken into account in the published
analyses, based on specific models of quark-hadron duality.
