  From soft-collinear effective theory one can derive a factorization formula
for the e+e- thrust distribution dsigma/dtau with tau = 1-T that is applicable
for all tau. The formula accommodates available O(alpha_s^3) fixed-order QCD
results, resummation of logarithms at NNNLL order, a universal nonperturbative
soft function for hadronization effects, factorization of nonperturbative
effects in subleading power contributions, bottom mass effects and QED
corrections. We emphasize that the use of Monte Carlos to estimate
hadronization effects is not compatible with high-precision, high-order
analyses. We present a global analysis of all available e+e- thrust data
measured at Q = 35 to 207 GeV in the tail region, where a two-parameter fit can
be carried out for alpha_s(m_Z) and Omega_1, the first moment of the soft
function. To obtain small theoretical errors it is essential to define Omega_1
in a short-distance scheme, free of an O(Lambda_QCD) renormalon ambiguity. We
find alpha_s(m_Z) = 0.1135 +- (0.0002)_expt +- (0.0005)_Omega_1 +-
(0.0009)_pert with chi^2/dof = 0.9.
