In this paper, two novel prediction-based haptic data reduction and transmission techniques are presented to reduce data traffic in telementoring systems. The prediction approach relies on the least-squares method and median filtering to reduce the number of packets transmitted, and efficiently reconstruct unsuccessfully received data samples. Knowledge from human haptic perception is also used and incorporated into the architecture of the two methods. The techniques are initially evaluated in a basic experimental setting to validate their performance. Their application in a haptic-enabled telementoring surgery simulation is also demonstrated. The experimental results prove the effectiveness of the proposed approach as haptic data packets can be reduced by as much as 96% while preserving the overall quality of the telementoring environment.