Afterimage-like effects modulate the responses of fly wide-field motion-sensitive cells following adaptation to stationary or slowly moving patterns. The origin of these afterimages is unclear. They have been interpreted as either the result of adaptation in the early visual system or as a direct consequence of the correlation scheme of motion detection. Using a combination of intracellular recording and computer modelling, we find that afterimage-like effects cannot be satisfactorily explained by a simple version of the correlation model previously proposed by Egelhaaf and Borst (J. Opt. Soc. Am. A 6 (1) (1989) 116). We propose a modified variant of the correlation model featuring a short delay filter and temporal high-pass filtering prior to motion correlation. Our model gives superior predictions of afterimage-like effects induced by a range of stimuli. Our model also predicts changes in cells' image step responses following exposure to motion, suggesting that previous experimental evidence for the "shortening delay" theory of motion adaptation (Biol. Cybern. 54 (1986) 223; Visual Neurosci. 14 (4) (1997) 741) should be re-interpreted in terms of afterimage effects.