  Physical quantities in QCD are independent of renormalization scheme (RS),
but that exact invariance is spoiled by truncations of the perturbation series.
"Optimization" corresponds to making the perturbative approximant, at any given
order, locally invariant under small RS changes. A solution of the resulting
optimization equations is presented. It allows an efficient algorithm for
finding the optimized result. Example results for R(e+e-)=3(Sum q_i^2)(1+R) to
fourth order (NNNLO) are given that show nice convergence, even down to
arbitrarily low energies. The Q=0 "freezing" behaviour, R=0.3+/-0.3, found at
third order is confirmed and made more precise; R=0.2+/-0.1. Low-energy results
in the MS-bar scheme, by contrast, show the typical pathologies of a
non-convergent asymptotic series.
