For the human observer, it can be difficult to follow the motion of small objects, especially when they move against background clutter. In contrast, insects efficiently do this, as evidenced by their ability to capture prey, pursue conspecifics, or defend territories, even in highly textured surrounds. We here recorded from target selective descending neurons (TSDNs), which likely subserve these impressive behaviors. To simulate the type of optic flow that would be generated by the pursuer’s own movements through the world, we used the motion of a perspective corrected sparse dot field. We show that hoverfly TSDN responses to target motion are suppressed when such optic flow moves syn-directional to the target. Indeed, neural responses are strongly suppressed when targets move over either translational sideslip or rotational yaw. More strikingly, we show that TSDNs are facilitated by optic flow moving counterdirectional to the target, if the target moves horizontally. Furthermore, we show that a small, frontal spatial window of optic flow is enough to fully facilitate or suppress TSDN responses to target motion. We argue that such TSDN response facilitation could be beneficial in modulating corrective turns during target pursuit.