Even though Application Level Multicast (ALM) protocols are proposed as an efficient alternative to the classical IP multicast model, they still suffer from the same rearrangement overhead problem. Indeed, when a member joins or leaves the multicast session, a part of the overlay tree should be rearranged. This rearrangement overhead can significantly disturb the fluidity of the application data stream received by other members. In addition, the efficiently of the constructed overlay tree depends entirely on the honesty and the cooperation of all participating members. However such behavior cannot be guaranteed and some selfish and non-cooperative nodes may take profit from the honesty of other members in the overlay. In this paper we present a new technique, called Membership Duration Aware ALM (MDA technique), that takes advantage of the announced membership duration of each new joining member in order to construct a more stable and robust overlay trees. Our technique can be used together with any existing centralized or distributed ALM protocol to reduce the overall rearrangement overhead. Simulation results confirm the efficiency of our technique when applied to both centralized and distributed ALM protocol. Then, we analyze in depth the impact of cheating nodes on the performances and the stability of overlay trees constructed by our MDA-ALM protocol.