The virtual path concept has been proposed as the key technique in improving the transmission efficiency in ATM networks. Changing the bandwidth of a virtual path, by a step at a time, has been shown to successfully enhance the transmission efficiency compared to the fixed bandwidth scheme. Therefore how to appropriately select a step size which causes a trade-off between the transmission efficiency and the normalised processing load, becomes an important issue. The authors propose a flexible and effective bandwidth control algorithm, which is capable of dynamically selecting a proper step size according to traffic types, network conditions, and the bandwidth-demand factor of each traffic type. Performance measures of the network, using this dynamic bandwidth-allocation scheme are analysed. Two examples are provided for illustration. The first shows that the proposed algorithm is capable of improving the transmission efficiency, even compared to the scheme with optimal fixed step size. The other shows that the normalised processing loads of both traffic types are significantly reduced without degradation in transmission efficiency.