Abstract. An increasing number of networking applications involve multiple participants and are therefore best supported by multicasting. Where a multicast application consumes high bandwidth, it is important to min-imise the effect on the network by offering economical multicast routes. Many new applications made possible by networks based on ATM involve real-time components and are therefore also delay-sensitive. This paper discusses reasonably simple techniques for multicast routing which tackle both of these constraints, that is:first, the route mak es efficient use of network resources and, secondly , delays to all recipients are kept within a bound. The problem is NP-complete, so we present heuristics which build up a directed graph containing potential routing solutions and use a greedy approach to select a solution from that graph. The heuristics are discussed and evaluated and are shown to offer good results for a variety of situations including both large and small multicast groups. Our approach is also compared with a previous solution to this problem, which has a greater time complexity.