  A method of resummation of truncated perturbation series, related to diagonal
Pad\'e approximants but giving results independent of the renormalization
scale, was developed more than ten years ago by us with a view of applying it
in perturbative QCD. We now apply this method in analytic QCD models, i.e.,
models where the running coupling has no unphysical singularities, and we show
that the method has attractive features such as a rapid convergence. The method
can be regarded as a generalization of the scale-setting methods of Stevenson,
Grunberg, and Brodsky-Lepage-Mackenzie. The method involves the fixing of
various scales and weight coefficients via an auxiliary construction of
diagonal Pad\'e approximant. In low-energy QCD observables, some of these
scales become sometimes low at high order, which prevents the method from being
effective in perturbative QCD where the coupling has unphysical singularities
at low spacelike momenta. There are no such problems in analytic QCD.
