  Previously developed Pade-related method of resummation for QCD observables,
which achieves exact renormalization-scale-invariance, is extended so that the
scheme-invariance is obtained as well. The dependence on the leading scheme
parameter $c_2$ is eliminated by a variant of the method of the principle of
minimal sensitivity. The subleading parameter $c_3$ in the approximant is then
fixed in such a way that the correct known location of the leading infrared
renormalon pole is reproduced. Thus, $beta$-functions which go beyond the last
perturbatively calculated order in the observable are used. The
$\beta$-functions in the approximant are quasianalytically continued by Pade
approximants. Two aspects of nonperturbative physics are accounted for in the
presented resummation: a mechanism of quasianalytic continuation from the weak-
into the strong-coupling regime, and the (approximant-specific) contribution of
the leading infrared renormalon. The case of the Bjorken polarized sum rule is
considered as a specific example of how the method works.
