We investigate joint transmission power control and playout buffer control for packetized media streaming over wireless links. We propose a novel model formulation that tracks the play/freeze duration and play/freeze switch jitter to control the transmission power and playout rate (1 or 0, i.e., play or rebuffer). The model is especially appropriate for audio/music streaming. The optimal joint control is obtained using a Dynamic Programming approach to balance the average power used against achieved quality of service (QoS), reflecting play/freeze duration and jitter frequency. We also investigate two key special cases, where either only power control or rebuffer control is exercised; we obtain certain useful provable structural properties of these individual side controls. Based on those, we also design a lowcomplexity heuristic control that 'mimics' the obtained structural properties of the optimal ones. Through simulation we see that the developed controls can achieve substantially higher performance over standard benchmark schemes. ‡ This work was conducted when Yan Li was affiliated with the Electrical Engineering Department at Stanford University. This paper is an extended journal version of the conference paper [22]. music on cellular phones, streamed from Internet servers via base stations or wireless access points.A major challenge in supporting high-quality audio/video streaming over wireless links is coping with the stochastically time-varying nature of the wireless channel. Fast fading, slow shadowing, path loss, and overall interference all degrade the signal quality at the receiver. These factors both decrease the average channel throughput and may also induce deep variations on it. For streaming applications, such variations can be very detrimental to the quality of service (QoS), since audio/video is to be