  The semihadronic tau decay width allows a clean extraction of the strong
coupling constant at low energies. We present a modification of the standard
"contour improved" method based on a derivative expansion of the Adler
function. The approach eliminates ambiguities coming from the existence of
different integral expressions for the semihadronic tau decay ratio. Compared
to the standard method, renormalization scale dependence is by more than a
factor two weaker in modified contour improved perturbation theory. The last
term of the expansion is reduced, and renormalization scheme dependence remains
approximately equal. The extracted QCD coupling at the tau mass scale is by
2$%$ lower than the "contour improved" value. We find
$\alpha_s(M_Z^2)=0.1211\pm 0.0010$.
