The leaky bucket, a credit management system that allows cells to enter the network only if sufficient credit is available, is considered. Motivation for an in-depth study of dynamic control algorithms, to avoid congestion in high-speed networks under time varying traffic statistics, is provided. The need for real-time traffic measurements and dynamic control actions for long-lived connections is demonstrated. In particular, it is shown through simulations that implementing access control algorithms based on the bandwidth allocation procedures only at connection setup is not sufficient for congestion-free operation of the network. It is further shown that if the bandwidth allocation and the leaky bucket parameters are not dynamically adjusted, the performances of the connections depend on their initial parameters and can be very undesirable as the traffic parameters change over time. Moreover, if corrective actions are not taken, congestion may build up in the network even in the presence of leaky buckets. The simple dynamic approach proposed limits the congestion periods in the network to the time scales of the connection-level controls. Therefore, the probability of many connections sending excess traffic into the network at the same time is greatly reduced, alleviating the congestion problem.>