It is known that people misperceive scenes they see during rapid eye movements called saccades. It has been suggested that some of these misperceptions could be an artifact of neurophysiological processes related to the internal remapping of spatial coordinates during saccades. Alternatively, we have recently suggested, based on a computational model, that transsaccadic misperceptions result from optimal inference. As one of the properties of the model, sudden object displacements that occur in sync with a saccade should be perceived as contracted in a non-linear fashion. To explore this model property, here we use computer simulations and psychophysical methods first to test how robust the model is to close-to-optimal approximations and second to test two model predictions: (a) contracted transsaccadic perception should be dimension-specific with more contraction for jumps parallel to the saccade than orthogonal to it, and (b) contraction should rise as a function of visuomotor noise. Our results are consistent with these predictions. They support the idea that human transsaccadic integration is governed by close-to-optimal inference.