  The Brodsky--Lepage--Mackenzie procedure is sequentially and unambiguously
extended to any fixed order of perturbative QCD beyond the so called
``large--\beta_0 approximation''. As a result of this procedure, the obtained
perturbation series looks like a continued-fraction representation. A
subsequent generalization of this procedure is developed, in order to optimize
the convergence of the final series, along the lines of the Fastest Convergence
Prescription. This generalized BLM procedure is applied to the Adler D function
and also to R_{e^+e^-} in QCD at N$^3$LO. A further extension of the sequential
BLM is presented which makes use of additional parameters to optimize the
convergence of the power-series at any fixed order of expansion.
