Low-level motion processing in the primate visual system involves two stages. The first stage (in V1) contains specialised motion sensors which respond to local retinal motion, and the second stage (in MT) pools local signals to encode rigid surface motion. Recent psychophysical research shows that motion signals influence the perceived position of an object (motion-induced position shift, MIPS). In the present paper we investigate the role played by the two processing stages in generating MIPS. We compared MIPS induced by single grating components (Gabor patches) to MIPS induced by plaids created by combining pairs of components. If motion signals at the lowest level of motion analysis (V1) influence position assignment, MIPS from plaids should reflect the position shift induced by each component when presented separately. On the other hand, if signals generated in MT (or later) influence perceived position, then MIPS from plaids should be consistent with a motion integration computation on the components. Results showed that MIPS from plaids is larger than the MIPS obtained from individual components, and can be explained by the output of an integration process that combines intersection-of-constraints and vector-sum computations.