We suggest that naive perturbation theory up to 0(alpha(s)(3)) underestimates the theoretical prediction for R-tau = Gamma[tau(-) --> nu(tau) + hadrons]/Gamma[tau(-) --> nu(tau)e-<(nu)over bar>(e)]. We use Pade Summation (PS) and find alpha(s)(M-z) = .313 (9). Using the new 4-loop QCD beta-function, we find alpha(s)(M-z) = .1172 (11) in agreement with recent values.