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ATM networks provide constant bit rate (CBR) services to all the variable bit rate (VBR) sources. In CBR services a fixed value of bandwidth is allocated for each connection at the peak rate. MPEG video is VBR traffic, because of the variable bandwidth requirements; there is potential bandwidth wastage with peak-rate bandwidth assignment. A method to alleviate this situation is proposed. The method dynamically allocates the spare bandwidth to frames whose frame length exceeds the negotiated value for each connection. The smaller the extra number of bandwidth units needed by the input frame, the greater is the priority for the connection to be assigned extra available bandwidth. This bandwidth algorithm when combined with the traffic smoothing technique like usage of buffers gives a good improvement in the quality of service. The benefit of this prioritized order of spare bandwidth assignment for all existing connections is that bandwidth requirements for the largest possible number of connections can be satisfied. The algorithm overcomes the bottleneck of the CBR service and the bandwidth utilization can be increased.