  Infrared power corrections for the average thrust < T > in e+e- annihilation
are analyzed in the framework of renormalon resummation, motivated by analogy
with the skeleton expansion in QED and the BLM approach. Performing the
``massive gluon'' renormalon integral a renormalization scheme invariant result
is obtained. We find that a major part of the discrepancy between the known
next-to-leading order (NLO) calculation and experiment can be explained by
resummation of higher order perturbative terms. This fact does not preclude the
infrared finite coupling interpretation with a substantial 1/Q power term.
Fitting the regularized perturbative sum plus a 1/Q term to experimental data
yields alpha_s^{MSbar}(M_Z)=0.110 \pm 0.006.
