Information about the position of our hand is provided by multisensory signals that are often not perfectly aligned. Discrepancies between the seen and felt hand position or it's movement trajectory engage the processes of i) multisensory integration, ii) sensory recalibration, and iii) motor adaptation, which adjust perception and behavioral responses to apparently discrepant signals. To foster our understanding of the co-emergence of these three processes we probed their short-term dependence on multisensory discrepancies in a visuo-motor task that has served as a model for multisensory perception and motor control previously. We found that the well-established integration of discrepant visual and proprioceptive signals is tied to the immediate discrepancy and independent of the outcome of the integration of discrepant signals in immediately preceding trials. However, the strength of integration was context dependent, being stronger in an experiment featuring stimuli that covered a smaller range of visuo-motor discrepancies (±15°) compared to one covering a larger range (±30°). Both sensory recalibration and motor adaptation for non-repeated movement directions were absent after two bimodal trials with same or opposite visuo-motor discrepancies. Hence our results suggest that short-term sensory recalibration and motor adaptation are not an obligatory consequence of the integration of preceding discrepant multisensory signals.