Using a multi-electrode nerve-signal recording cuff and a method of signal processing described previously, activity in axons with different propagation velocities can be distinguished, and the relative amplitude of the small-fibre signals increased. This paper is, largely, an analysis of the selectivity and noise of this system though impedance measurements from an actual cuff are included. The signal processor includes narrow band-pass filters. It is shown that the selectivity and noise both increase with the centre frequencies of these filters. A convenient approach is to make the filter frequencies inversely related to the artificial time delays so that the filter ‘Q’s are approximately constant and the noise densities are equal for all velocity filters. Numerical calculations, using formulae for this system and for the conventional tripole, based on a fixed cuff size and tissue resistivity, find the number of action potentials per second that must pass through the cuff so that the signal power equals the noise power. For slow fibres (20 m/s), the rate is 14 times lower for the multi-electrode cuff than the tripole, a significant advantage for recording from these fibres.