Techniques of service-rate controls in ATM switches are described, and apparatus for their implementation are devised. The techniques fall in two categories: frequency domain controls, and time-domain controls. The regulators control the service rate on a per-class basis or on a per-connection basis. Some class regulators operate at very high speeds of the order of several gigabits per second and cover a medium number of classes, 32 for example. Other regulators operate at high speeds of the order of several-hundred megabits per second, and cover a very large number of classes, e.g., 10000. A compound regulator which combines both types of regulators is also described. The compound regulators extend the range of controllable classes considerably, covering some 200,000 classes. The main advantages of the regulators of the invention are simplicity, robustness, and high performance.