  We directly fit the experimentally measured energy dependence of the average
value of 1-Thrust, <1-T>, over the e^+e^- centre-of-mass energy range Q=14 -
172 GeV to the QCD expectation obtained by integrating up the evolution
equation for d<1-T>/dlog Q in terms of <1-T>. We fit for Lambda_QCD,
uncalculated O(alpha_S^3) and higher perturbative corrections parameterized by
the scheme invariant rho_2, and the parameter lambda which characterizes the
magnitude of the leading 1/Q power corrections anticipated for <1-T>. A
3-parameter fit yields Lambda_QCD=245^{+20}_{-17} MeV, rho_2=-16\pm 11 and
lambda=0.27^{+0.12}_{-0.10} GeV, equivalent to alpha_S(M_Z)=0.1194 \pm 0.0014.
In this approach, there is no error associated with the choice of the
renormalization scale mu.
