  Perturbative QCD with nf flavours of massless quarks becomes simple in the
hypothetical limit nf -> 16.5, where the leading beta-function coefficient
vanishes. The Banks-Zaks (BZ) expansion in a0=(8/321)(16.5-nf) is
straightforward to obtain from perturbative results in MSbar or any
renormalization scheme (RS) whose nf dependence is `regular.' However,
`irregular' RS's are perfectly permissible and should ultimately lead to the
same BZ results. We show here that the `optimal' RS determined by the Principle
of Minimal Sensitivity does yield the same BZ-expansion results when all orders
of perturbation theory are taken into account. The BZ limit provides an arena
for exploring optimized perturbation theory at arbitrarily high orders. These
explorations are facilitated by a `master equation' expressing the optimization
conditions in the fixed-point limit. We find an intriguing strong/weak coupling
duality a -> a*^2/a about the fixed point a*.
