Max-min fair bandwidth allocation is desirable because it protects well-behaved flows while keeping network utilization high. Achieving and maintaining absolute global max-min fairness at finite flow granularity is improbable. Moreover, computing and communicating max-min fair rates has a significant overhead. In this paper, we define the notion of /spl epsiv/-fairness and derive the conditions for flow rates to be /spl epsiv/-fair. We describe a technique where max-min fairness is computed at the level of flow groups while /spl epsiv/-fairness is provided to individual flows. Using /spl epsiv/-fairness allows the network administrator to control the degree of fairness with an overhead proportional to the degree. An important implication of our technique is that traffic-pattern knowledge can be used to reduce overhead.