The loss and delay experienced by packets travelling along an Internet network path are mainly governed by the characteristics of a bottleneck link, such as available data rate and queue size. In this work, we propose a framework for rate-distortion optimized packet scheduling with adaptive rate control for media streaming over bandwidth-constrained bottleneck links. The framework computes optimal packet schedules while continuously adapting its instantaneous rate to the following three factors: the available data rate and the current queue size on the bottleneck link, and the congestion that packets transmitted under the schedules will create on the bottleneck link. Experimental results demonstrate that our framework does not lose in rate-distortion performance over rate-distortion optimized packet scheduling without strict rate control, while producing at the same time a much smoother instantaneous rate feeding the bottleneck queue. This in turn contributes to fairness to other flows sharing the bottleneck link and causes less variations in queue size, thereby avoiding queue overflow and unnecessarily long packet delays on the bottleneck link.