  The new result for the third-order QCD corrections to R_{e^+e^-}, unlike the
old, incorrect result, is nicely compatible with the
principle-of-minimal-sensitivity optimization method. Moreover, it leads to
infrared fixed-point behaviour: the optimized couplant, alpha_s/pi, for R(e+e-)
does not diverge at low energies, but "freezes" to a value 0.26 below about 300
MeV. This provides some direct theoretical evidence, purely from perturbation
theory, for the "freezing" of the couplant -- an idea that has long been a
popular and successful phenomenological hypothesis. We use the "smearing"
method of Poggio, Quinn, and Weinberg to compare the resulting theoretical
prediction for R(e+e-) with experimental data down to the lowest energies, and
find excellent agreement.
