Increasing uncontrolled best-effort traffic deteriorates the ability of TCP to control congestion and is a source of high drop rates. This paper proposes an efficient congestion avoidance mechanism (ECAM) suitable for uncontrolled unicast and multicast best-effort flows. ECAM relies on and enhances a previous congestion avoidance mechanism for non-reliable flows that we have proposed previously. The key reason to the generality of our mechanism is the decoupling of congestion control from reliability through the use of source quench-like congestion feedback to the senders. As one of the main causes for high packet loss rates in the Internet is the lack of early notification of network congestion, we use active queue management techniques that have been developed to cope with this problem. Hence, we originally adapt random early detection (RED) and early congestion notification (ECN) for UDP in order to allow the UDP flows to be adaptive to network dynamics. We demonstrate through simulation that ECAM significantly reduces packet loss, enhance UDP to fairly coexist with TCP flows and provides an efficient and simple solution to congestion avoidance.