Whilst everyday interactions with objects often involve multiple tactile contacts, integration of tactile signals remains poorly understood. Here we characterise the integration process of tactile motion on multiple fingerpads. Across four experiments, participants averaged the direction of two simultaneous tactile motion trajectories delivered to different fingerpads. Averaging performance differed between within- and between-hands in terms of sensitivity and precision but was unaffected by somatotopic proximity between stimulated fingers. The sensitivity to the average direction was influenced by the discrepancy between individual motion signals, but only for within-hand conditions. This was explained by a model, in which the "virtually leading finger" received a higher perceptual weighting. Precision was greater in between-hand compared to within-hand conditions. While biased weighting accounted for differences in sensitivity, it was not sufficient to explain the difference in precision, implying additional sensory limitations during within-hand integration. We suggest that unimanual integration is limited and thus exploits a "natural" cognitive prior involving a single object moving relative to the hand to maximise information gain.