Scale setting for αs beyond leading order

We present a general procedure for applying the scale-setting prescription of Brodsky, Lepage and Mackenzie to higher orders in the strong coupling constant as. In particular, rye show how to apply this prescription when the leading coefficient or coefficients in a series in a, are anomalously small. We give a general method for computing an optimum scale numerically, within dimensional regularization, and in cases when the coefficients of a series are known. We find significant corrections to the scales for Re+e-, Gamma (B --> X(u)e<(<nu>)over bar>), Gamma (t --> bW), and the ratios of the quark pole to (MS) over bar and lattice bare masses.