Given a video stream delivering system deployed on a multicast tree, which is embedded in a multi-channel multi-radio wireless mesh network, our problem is concerned about how to allocate interference-free channels to tree links and maximize the number of serviced mesh clients at the same time. In this paper, we propose a channel allocation heuristic algorithm based on best-first search and backtracking techniques. The experimental results show that our BFB based CA algorithm outperforms previous methods such as DFS and BFS based CA methods. This superiority is due to the backtracking technique used in BFB approach. It allows previous channel-allocated links to have feasibility to select the other eligible channels when no conflict-free channel can be found for the current link during the CA process. In addition to that, we also propose a tree refinement method to enhance the quality of channel-allocated trees by adding uncovered destinations at the cost of deletion of some covered destinations. Our aim of this refinement is to increase the number of serviced mesh clients. According to our simulation results, it is proved to be an effective method for improving multicast trees produced by BFB, BFS and DFS CA algorithms.