  We use an Effective Charges (ECH) method to extract Lambda-MS-bar, and hence
alpha_s(M_z), from event shape moments in e+e- annihilation. We compare these
results with ones obtained using standard MS-bar perturbation theory. The ECH
method at NLO is found to perform better than standard MS-bar perturbation
theory when applied to means of event shape observables. For example, when we
apply the NLO ECH method to <1-T> we get alpha_s(M_z)=0.1193\pm0.0003. However
ECH at NNLO is found to work less well than ECH at NLO, and the ECH method also
fails to describe data for higher moments of event shapes. We attempt to
explain this by considering the ECH beta-function as an asymptotic series. We
also examine the effect of adding two different models for non-perturbative
power corrections to the perturbative approximation given by the ECH method and
MS-bar perturbation theory. Whilst only small power corrections are required
when using ECH at NLO, it is found that these models are insufficient to
couteract the undesirable behaviour of ECH at NNLO.
