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A flying insect must travel to find food, mates and sites for oviposition, but for a small animal in a turbulent world this means dealing with frequent unplanned deviations from course. We measured a fly's sensory-motor impulse response to perturbations in optic flow. After an abrupt change in its apparent visual position, a fly generates a compensatory dynamical steering response in the opposite direction. The response dynamics, however, may be influenced by superimposed background velocity generated by the animal's flight direction. Here we show that constant forward velocity has no effect on the steering responses to orthogonal sideslip perturbations, whereas constant parallel sideslip substantially shortens the lags and relaxation times of the linear dynamical responses. This implies that for flies stabilizing in sideslip, the control effort is strongly affected by the direction of background motion.