  We present a new framework for the extraction of the strong coupling from
hadronic \tau decays through finite-energy sum rules. Our focus is on the
small, but still significant non-perturbative effects that, in principle,
affect both the central value and the systematic error. We employ a
quantitative model in order to accommodate violations of quark-hadron duality,
and enforce a consistent treatment of the higher-dimensional contributions of
the Operator Product Expansion to our sum rules. Using 1998 OPAL data for the
non-strange isovector vector and axial-vector spectral functions, we find the
n_f=3 values \alpha_s(m_\tau^2)=0.307+-0.019 in fixed-order perturbation
theory, and 0.322+-0.026 in contour-improved perturbation theory. For
comparison, the original OPAL analysis of the same data led to the values
0.324+-0.014 (fixed-order) and 0.348+-0.021 (contour-improved).
