The NP-hard QoS Multicast Routing (QoSMR) is one of the most challenging problems in recent networks. In this paper, we investigate the QoSMR as well as its different existing formulations. We analyze the limitations of these formulations and propose a novel one. The main advantage of our formulation is that it considers not only the quality of the multicast subgraph formed by the computed paths, but also takes into account the end-to-end quality of each of these paths. Moreover, we study the state-of-the-art proposal for solving the QoSMR problem and show that the well-known MAMCRA algorithm can be very expensive in computation time. Therefore, we propose two efficient heuristics based on the computation of shortest paths. Extensive simulations are performed, and obtained results prove that these fast heuristics have bounded response time and find satisfying solutions for the QoS requirements.