We develop model-independent methods for characterizing the reliability of neural spike trains in response to brief stimuli. Through this approach we measure the discriminability of similar stimuli based on the real-time response of a single neuron in much the same way that modern psychophysical techniques measure the discrimination performance of the whole animal. Extending these techniques, we quantify discriminability as a function of time after stimulus presentation, so that it is possible to compare the measured reliability of the neuron to its theoretical limit predicted from signal transduction and noise levels in the sensory periphery. The methods are applied to a wide-field movement-sensitive neuron (H1) in the visual system of the blowfly Calliphora vicina, where we also record from the photoreceptor cells that provide the sensory input to H1. From an analysis of neural responses to wide-field stepwise movements of various step sizes we find the following. (1) One or two spikes are sufficient to encode just noticeable differences of approximately one-tenth the angular spacing between photoreceptors, comparable to the hyperacuity regime observed in humans. (2) Discriminability improves upon observation of successive spikes as if the interspike intervals carried independent information. Coding seems orderly and analogue in the sense that we find no indication of information being transmitted in complex combinations of spike intervals. (3) As a result of neural refractoriness the real neuron's performance is significantly better than that of a neuron generating spikes according to a Poisson process at the same firing rate. (4) Over behaviourally relevant time intervals following the movement step, that is up to about 30-40 ms, the discrimination performance of the neuron is close to that of an ideal observer who extracts movement information from all the photoreceptor cells in the field of stimulation. Beyond this time the neuron's performance relative to the ideal observer decreases significantly.