Streaming video over the best-effort Internet raises some challenging issues. The available bandwidth and packet transmission delays are often subject to severe changes. As a consequence, a significant ratio of video packets is dropped by network routers because of lack of capacity on congested links. The impacts of video packet drops on the observed quality at receiver side may vary from unnoticed to unacceptable. This is due to the different values of each video packet for the decoding process at the receiver. Classical queueing disciplines do not have the ability to distinguish between different packet values. It is often the case that a packet of higher value is dropped, in favor of a lower valued packet. The value of a packet is measured in terms of the induced distortion, when the packet is not received correctly. In this paper, we introduce an application-specific queueing system, which drops packets in a size-distortion optimized manner. Out of all packets present in the queue, the system selects the packets to be dropped, if necessary, in order to meet a queue size constraint while minimizing the overall distortion. Important improvements in video quality for the receiver, and an efficient utilization of the available bandwidth have been observed throughout different simulations.