  It is shown that the previously noted extreme perturbative instability of the
longitudinal structure function F_L(x,Q^2) in the small Bjorken-$x$ region, is
a mere artefact of the commonly utilized `standard' gluon distributions. In
particular it is demonstrated that using the appropriate -- dynamically
generated -- parton distributions at NLO and NNLO, F_L(x,Q^2) turns out to be
perturbatively rather stable already for Q^2 $\geq$ O(2-3 GeV^2).
