  A recent extension of a variationally optimized perturbation, combined with
renormalization group properties in a straightforward way, can provide
approximations to nonperturbative quantities such as the chiral symmetry
breaking order parameters typically. We apply this to evaluate, up to third
order in this modified perturbation, the ratio Fpi/Lambda, where Fpi is the
pion decay constant and Lambda the basic QCD scale in the modified MS scheme.
Using experimental Fpi input value we obtain Lambda(nf=2) ~ 255_{-15}^{+40}
MeV, where quoted errors are estimates of theoretical uncertainties of the
method. This compares reasonably well with some recent lattice simulation
results. We briefly discuss prospects (and obstacles) for extrapolation to
alpha_S(mu) at perturbative mu values.
