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An efficient smoothing scheme for the real-time transmission of MPEG-1 transcoded video over 'best-effort' IP networks is presented. The scheme uses intelligent partitioning and multiplexing of the packetised bit stream. Bit-rate smoothing is achieved by partitioning packets according to their picture type (I, P or B). Subsequently, the partitioned packets are multiplexed in such a way that each packet from an anchor (I and P) picture is followed by two packets from B-pictures. The proposed scheme smooths the bit rate of the encoded video, making it more suitable for adaptive video streaming applications. In such applications, the transmission bit rate is varied so as to adapt to the available network bandwidth. The scheme reorganises the transmission order of the packets, spreading the less important packets from the B-pictures into the more important packets from the anchor pictures. This indicates a reduction in the likelihood of losing more important anchor packets as the bandwidth bottleneck increases, implying an improvement in the quality of transmitted video. A variety of simulations results are presented to demonstrate these points.