Tactile perception is inhibited during goal-directed reaching movements (sensory suppression). Here, participants performed simple reaching or exploratory movements (where contact with the table surface was maintained). We measured tactile discrimination thresholds for vibratory stimuli delivered to participants’ wrists while executing the movement, and while at rest. Moreover, we measured discrimination performance (in a same vs. different task) for the materials covering the table surface, during the execution of the different movements. The threshold and discrimination tasks could be performed either singly or together, both under active movement and passive conditions (i.e., no movement required, but with tactile stimulation). Thresholds measured at rest were significantly lower than thresholds measured during both active movements and passive touches. This provides a clear indication of sensory suppression during movement execution. Moreover, the discrimination data revealed main effects of task (single vs. dual), movement execution type (passive vs. active), and movement type (reach vs. exploration): Discrimination performance was significantly higher under conditions of single-tasking, active movements, as well as exploratory movements. Therefore, active movement of the hand with the purpose of gaining tactual information about the surface of the table gives rise to enhanced performance, thus suggesting that we feel more when we need to; It would appear that tactual information is prioritized when relevant for the movement being executed.