— Telepresence systems are often deployed in scenarios where communication bandwidth is limited. Consequently, data exchanged between operator and teleoperator has to be reduced. In case of haptic telepresence, data reduction has an influence on the stability of the overall system. This paper provides a step towards a systematic framework for communication data bandwidth reduction in haptic telepresence systems discussing stability for a class of lossy data reduction (LDR) algorithms. Simulation and experimental results validate the efficacy.