  We consider the flavour non-singlet Reggeon within the context of
perturbative QCD. This consists of ladders built out of ``reggeized'' quarks.
We propose a method for the numerical solution of the integro-differential
equation for the amplitude describing the exchange of such a Reggeon. The
solution is known to have a sharp rise at low values of Bjorken-x when applied
to non-singlet quantities in deep-inelastic scattering. We show that when the
running of the coupling is taken into account this sharp rise is further
enhanced, although the Q^2 dependence is suppressed by the introduction of the
running coupling. We also investigate the effects of simulating
non-perturbative physics by introducing a constituent mass for the soft quarks
and an effective mass for the soft gluons exchanged in the t-channel.
