  Different ways exist to obtain the elements of the $\{\beta \}$-expansion for
renormgroup invariant quantities. Here we consider independent confirmation
within the standard QCD of a number of our results [1] for the values of
elements of this expansion for the nonsinglet Adler $D_A$-function, Bjorken
polarized sum rules $S^{Bjp}$ up to the order N$^4$LO. We suggest an approach
to estimate the results of high order QCD calculations using a smaller number
of diagrams of the specific type. This type is based on a proposed
generalization of Naive NonAbelianization.
