Establishing a multicast tree in a point-to-point network of switch nodes, such as a wide-area ATM network, is often modeled as the NP-complete Steiner problem in networks. In this paper, we study algorithms for nding e cient multicast trees in the presence of constraints on the copying ability of the individual switch nodes in the network. We refer to this problem as the degree-constrained multicast tree problem and model it as the degree-constrained Steiner problem in networks. Steiner heuristics for the degree-constrained case are proposed and their simulation results for sparse, point-to-point networks are presented. The results are compared with respect to their quality of solution, cost (running time), and the number of test cases for which no solution could be found. The results of our research indicate that e cient multicast trees can be found in large, sparse networks with small multicast groups even with limited multicast capability in the individual switches. Some of the St...