While a considerable amount of research has been conducted to address QoS issues for best-effort Internet multimedia applications by utilising network-centric metrics (loss, delay, RTT, available bandwidth), less attention has been paid to the quality that is perceived by the users of the networked applications. Perceived quality of encoded multimedia is highly dependent on the time-varying characteristics of the content. We describe an approach for content-aware quality adaptation of multimedia sessions consisting of an ensemble of concurrent flows relevant to the presentation scenario. Using a quality metric that is based on the properties of the human visual perception process, we devise mechanisms that improve the overall session quality by efficiently apportioning the session bandwidth to the participating flows at appropriate adaptation times. We discuss the approach, propose suitable adaptation time scales and present results from trace-driven simulations that show the potential of content-aware quality adaptation.