During visual exploration of a scene, the eye-gaze tends to be directed toward more salient image-locations, containing more information. However, while performing non-visual tasks, such information-seeking behavior could be detrimental to performance, as the perception of irrelevant but salient visual input may unnecessarily increase the cognitive-load. It would be therefore beneficial if during non-visual tasks, eye-gaze would be governed by a drive to reduce saliency rather than maximize it. The current study examined the phenomenon of gaze-aversion during non-visual tasks, which is hypothesized to act as an active avoidance mechanism. In two experiments, gaze-position was monitored by an eye-tracker while participants performed an auditory mental arithmetic task, and in a third experiment they performed an undemanding naming task. Task-irrelevant simple motion stimuli (drifting grating and random dot kinematogram) were centrally presented, moving at varying speeds. Participants averted their gaze away from the moving stimuli more frequently and for longer proportions of the time when the motion was faster than when it was slower. Additionally, a positive correlation was found between the task's difficulty and this aversion behavior. When the task was highly undemanding, no gaze aversion behavior was observed. We conclude that gaze aversion is an active avoidance strategy, sensitive to both the physical features of the visual distractions and the cognitive load imposed by the non-visual task.