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 new approach has some advantages compared to contour-improved perturbation theory. The renormalization scale dependence is weaker by more than a factor of 2 and the last term of the expansion is reduced by about 10%, while the 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 +/- 0.0010.