The timing of action potentials relative to sensory stimuli can be precise down to milliseconds in the visual system, even though the relevant timescales of natural vision are much slower. The existence of such precision contributes to a fundamental debate over the basis of the neural code and, specifically, what timescales are important for neural computation. Using recordings in the lateral geniculate nucleus, here we demonstrate that the relevant timescale of neuronal spike trains depends on the frequency content of the visual stimulus, and that `relative', not absolute, precision is maintained both during spatially uniform white-noise visual stimuli and naturalistic movies. Using information-theoretic techniques, we demonstrate a clear role of relative precision, and show that the experimentally observed temporal structure in the neuronal response is necessary to represent accurately the more slowly changing visual world. By establishing a functional role of precision, we link visual neuron function on slow timescales to temporal structure in the response at faster timescales, and uncover a straightforward purpose of fine-timescale features of neuronal spike trains.