Models are developed and evaluated that are able to describe the response of blowfly photoreceptor cells to natural time series of intensities. Evaluation of the models is performed using an information theoretical technique that evaluates the performance of the models in terms of a coherence function and a derived coherence rate (in bit/s). Performance is gauged against a maximum expected coherence rate determined from the repeatability of the response to the same stimulus. The best model performs close to this maximum performance, and consists of a cascade of two divisive feedback loops followed by a static nonlinearity. The first feedback loop is fast, effectively compressing fast and large transients in the stimulus. The second feedback loop also contains slow components, and is responsible for slow adaptation in the photoreceptor in response to large steps in intensity. Any remaining peaks that would drive the photoreceptor out of its dynamic range are handled by the final compressive nonlinearity.