Most models devised to account for the excess galaxies seen in number magnitude counts invoke a large population of low-luminosity galaxies at moderate redshifts (or look-back times). Here we directly investigate the faint end of the luminosity function at moderate z (congruent-to 0.2) via deep R-band observations of the distant Abell cluster A963 made with the Hitchhiker parallel CCD camera on the WHT. By subtracting a 'mean field' component from the observed galaxy counts in the cluster area, we deduce the existence of a large dwarf population in the cluster, which gives rise to a significant excess over the mean, right down to the sample limit at m(R) congruent-to 24.5 (M(R) congruent-to - 16.5). The implied dwarf-galaxy luminosity function has a steep slope, alpha approximately - 1.8, in line with recent work on nearby clusters.