  We use recently calculated next-to-next-to-leading (NNLO) anomalous dimension
coefficients for the n=1,3,5,...,13 moments of the xF3 structure function in
nuN scattering, together with the corresponding three-loop Wilson coefficients,
to obtain improved QCD predictions for the moments. The Complete
Renormalization Group Improvement (CORGI) approach is used, in which all
dependence on renormalization or factorization scales is avoided by a complete
resummation of ultraviolet logarithms. The Bernstein Polynomial method is used
to compare these QCD predictions to the xF3 data of the CCFR collaboration.
Direct fits for LambdaMSbar(5), with Nf=5 effective quark flavours, over the
range 20<Q^2<125.9 GeV^2 were performed. We obtain LambdaMSbar(5)=202+54/-45
MeV, corresponding to the three-loop running coupling
alphas(MZ)=0.1174+0.0043-0.0043. Including target mass corrections as well we
obtain LambdaMSbar(5)=228+35/-36 MeV, corresponding to
alphas(MZ)=0.1196+0.0027-0.0031.
