Development of efficient multicasting algorithms which support a wide range of quality of service requirements is crucial to the successful deployment of multimedia applications. In this paper, we present a new class of low-cost, bounded delay multicast heuristics for integrated service networks. The heuristics use various techniques to find the solution to the multicast problem, if one exists. These heuristics are described and shown to be cycle free and of complexity O(z * n^2) where z is the number of multicast nodes and n is the number of nodes in the network. We also show that if no delay bound was violated during the construction of the tree, the proposed heuristics give an approximation that does not exceed in average the cost of the optimal solution by more than 5%.