Haptic interaction with virtual as well as real environments is much more demanding to the underlying network than traditional audio/ video communication. Because of very strict delay constraints imposed by the global control loop which is closed by the communication system very high packet rates are generated. Each packet typically carries a small amount of payload data leading to a significant packet header versus payload overhead. This paper presents a psychophysically motivated deadband transmission approach for multidimensional haptic data using the example of three dimensional haptic interaction. Packets are only generated and sent if the change in haptic variables exceeds the just noticeable difference of the human operator. The presented approach reduces packet rates in haptic systems by up to 90% without any perceivable reduction of immersiveness. To our knowledge the proposed approach is the first psychophysically motivated compression approach for multidimensional haptic data in literature.