Detection of targets that move within visual clutter is a common task for animals searching for prey or conspecifics, a task made even more difficult when a moving pursuer needs to analyze targets against the motion of background texture (clutter). Despite the limited optical acuity of the compound eye of insects, this challenging task seems to have been solved by their tiny visual system. Here we describe neurons found in the male hoverfly, Eristalis tenax, that respond selectively to small moving targets. Although many of these target neurons are inhibited by the motion of a background pattern, others respond to target motion within the receptive field under a surprisingly large range of background motion stimuli. Some neurons respond whether or not there is a speed differential between target and background. Analysis of responses to very small targets (smaller than the size of the visual field of single photoreceptors) or those targets with reduced contrast shows that these neurons have extraordinarily high contrast sensitivity. Our data suggest that rejection of background motion may result from extreme selectivity for small targets contrasting against local patches of the background, combined with this high sensitivity, such that background patterns rarely contain features that satisfactorily drive the neuron.