The brain integrates incoming sensory signals to a degree that depends on the signals’ redundancy. Redundancy—which is commonly high when signals originate from a common physical object or event—is estimated by the brain from the signals’ spatial and/or temporal correspondence. Here we tested whether verbally instructed knowledge of non-redundancy can also be used to reduce the strength of the sensory integration. We used a cursor-control task in which cursor motions in the frontoparallel plane were controlled by hand movements in the horizontal plane, yet with a small and randomly varying visuomotor rotation that created spatial discrepancies between hand and cursor positions. Consistent with previous studies, we found mutual biases in the hand and cursor position judgments, indicating partial sensory integration. The integration was reduced in strength, but not eliminated, after participants were verbally informed about the non-redundancy (i.e., the spatial discrepancies) in the hand and cursor positions. Comparisons with model predictions excluded confounding bottom-up effects of the non-redundancy instruction. Our findings thus show that participants have top-down control over the degree to which they integrate sensory information. Additionally, we found that the magnitude of this top-down modulatory capability is a reliable individual trait. A comparison between participants with and without video-gaming experience tentatively suggested a relation between top-down modulation of integration strength and attentional control.