In recent distributed multimedia applications such as multi-site teleconferencing, different video streams from different locations are distributed to a number of receivers via multicasting on the Internet, and each receiver simultaneously plays back these videos on his/her terminals. These multicast streams may often be delivered on the same bottleneck link, therefore they are likely to cause competition with each other for the limited bandwidth. In general, layered multicast is considered efficient for avoiding congestion by letting only the affected receivers degrade their receiving rates. However, in case of bandwidth competition by multiple layered multicast streams (inter-stream bandwidth competition), these receivers may choose different streams to be degraded, which may result in slow convergence and low utility of bandwidth. In this paper, we propose a protocol to coordinate those receivers in a distributed manner, for the fast convergence to an optimal layer subscription in the event of inter-stream bandwidth competition, based on application-specific priorities given by receivers to the layers. In our protocol, the number of messages exchanged in the event of congestion is considerably kept low based on tree topology information, obtained by a multicast tree inference technique. Simulation results have shown the effectiveness of our technique on networks with about 200 nodes.