We study the combination of the perceptual deadband (PD)-based haptic packet rate reduction scheme with the time domain passivity approach (TDPA) for time-delayed teleoperation and propose a novel energy prediction (EP) scheme that deals with the conservative behavior of the resulting controller. The PD approach leads to irregular packet transmission, resulting in degraded system transparency and reduced teleoperation quality when the PD approach is combined with the TDPA. The proposed method (PD+TDPA+EP) adaptively predicts the system energy during communication interruptions and allows for larger energy output. This achieves less conservative control and improves the teleoperation quality. Evaluation of the displayed impedance shows that the PD+TDPA+EP method achieves improved system transparency, both objectively and subjectively, when compared with related approaches from literature. According to a subjective user study, the PD+TDPA+EP method allows for a high packet rate reduction (up to 80 percent) without noticeably distorting the perceived interaction quality. We also show that the PD+TDPA+EP method is preferred over related approaches from literature in a direct comparison test. Thus, with the proposed PD+TDPA+EP method, a high data reduction and a high teleoperation quality are simultaneously achieved for time-delayed teleoperation.