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 ⩾ O ( 2 – 3 GeV 2 ) .