The cooperation of end users can be exploited to boost the performance of high-bandwidth multicast. While intraoverlay cooperation, the mechanism for cooperation within a single overlay (multicast group), has been extensively studied, little attention has been paid to inter-overlay cooperation. In this paper we explore the possibility and effects of cooperation among co-existing heterogeneous overlays in the context of live media streaming, where bandwidth is the bottleneck resource. To motivate such a kind of cooperation, we design a reputation-based incentive mechanism that differentiates user? streaming qualities based on the amount of data actually forwarded by individual users. This not only stimulates users to contribute as much forwarding bandwidth as possible, but also motivates those with spare bandwidths in resource-rich overlays to find downstream users in external, often resource-poor, overlays so as to accumulate more reputation scores. Under this mechanism, an adaptive bandwidth exporting/reclaiming algorithm is developed which allows users to dynamically allocate bandwidth according to the resource availability of multiple overlays. Simulation results are reported with enhanced system performance in terms of users? average media quality.