Efficient and low-delay exchange of hapticinformation plays a key role for the design of high-fidelity teleoperation systems that operate over real-world communication networks. In the presence of communication unreliabilities such as delay and packet loss, a combination of stability-ensuring control schemes and haptic data reduction approaches is essential to address the challenges from both the control and communication perspective. In this paper, we extend our previous one degree-of-freedom (DoF) solution to 3DoF that combines the time-domain passivity approach (TDPA) and the perceptual deadband-based (DB) haptic data reduction approach. We also extend the 1DoF energy compensation (EC) scheme to 3DoF for mitigating the control artifacts introduced by the inter-play of the TDPA and DB approaches. The 3DoF solution is analyzed in detail and verified through a real-world teleoperation setup. The performance of the proposed method and the existing solutions is compared though objective and subjective assessments. Experimental results show that by jointly considering the evaluated objective/subjective quality and the required packet rate, the proposed 3DoF solution with the EC scheme improves system performance significantly compared to the state-of-the-art solutions.