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We discuss how the renormalisation scheme ambiguities in QCD can be fixed,when two observables are related, by requiring the coefficients in theperturbative expansion relating the two observables to have their conformallimit values, i.e. to be independent of the $\beta$-function of therenormalised coupling. We show how the next-to-leading order BLM automaticscale fixing method can be extended to next-to-next-to-leading order to fixboth the renormalisation scale and $\beta_2$ in a unique way. As an example weapply the method to the relation between Bjorken's sum rule and $R_{e+e-}$ andcompare with experimental data as well as other scheme fixing methods.Comment: 14 pages LaTeX, uses revtex.sty, 1 encapsulated PostScript figur

Fixing the renormalization scheme in NNLO perturbative QCD using conformal limit arguments