Sensitivity to touch is reduced during movement; this tactile suppression is likely the result of a mechanism that suppresses self-generated movement consequences. We sought to determine whether tactile suppression is modulated by naturally evoked changes in movement speed driven by task precision demands (Exp.1), and by changes in predicted movement consequences (Exp.2). We measured suppression by comparing detection thresholds for a vibration applied to the finger during reach and at rest. In Experiment 1 we varied reach target size to create a speed-accuracy tradeoff, where participants decelerated more to smaller targets to accurately hit them. We theorized that the reduction in late-reach speed associated with higher precision demands might lead to a reduction in late-reach suppression, consistent with the literature showing a positive relationship between speed and suppression. Contrary to our hypothesis, we found suppression increased towards the end of the reach in all conditions, despite a significant decrease in reaching speed. We postulated this might be a de-emphasizing of the predicted tactile feedback associated with tapping the target. To test this, in Experiment 2 we paired a vibration consequence with a target of a certain colour. We found an increase in late-reach suppression for this target compared to a target of another colour with no associated consequence. Our results indicate that tactile suppression is temporally sensitive and increases as predicted consequences become more likely. We propose the positive correlation between movement speed and suppression previously reported may be driven by the predicted somatosensory consequences associated with increased movement speed.