Abstract: To improve the performance in terms of selectivity, responsiveness, and mean queueing delay for a connetion in ATM networks, a fuzzy leaky bucket method and apparatus is introduced that monitors and controls the sustainable cell rate of the connection utilizing a fuzzy increment controller (FIC) to dynamically adjust the value of the increment for the content of the leaky bucket incorporated for policing the connection. The adjustment of the increment by the fuzzy logic is accomplished through a set of linguistic rules based upon a domain knowledge. Two system parameters of the long-term mean cell rate and the short-term mean cell rate of the connection are fed into the fuzzy increment controller to adaptively calculate an appropriate increment value with an aim to achieve a better performance.