In this paper, we design a new heuristic for an important extension of the minimum power multicasting problem in ad hoc wireless networks^20,21. Assuming that each transmission takes a fixed amount of time, we impose constraints on the number of hops allowed to reach the destination nodes in the multicasting application. This setting would be applicable in time critical or real time applications, and the relative importance of the nodes may be indicated by these delay bounds. We design a filtered beam search procedure for solving this problem. The performance of our algorithm is demonstrated on numerous test cases by benchmarking it against an optimal algorithm in small problem instances, and against a modified version of the well-known Broadcast Incremental Power (BIP) algorithm ²⁰ for relatively large problems.