It has been shown that the problem of finding a broadcast routing tree with minimum total transmit power is NP-hard. Hence, developing a heuristic power-efficient algorithm is crucial. The seminal work in this area is the well-known broadcast incremental power (BIP) algorithm with a recent addition called embedded wireless multicast advantage (EWMA) algorithm. In this paper, we present yet another novel power-efficient algorithm for broadcast routing tree construction called greedy perimeter broadcast efficiency (GPBE) algorithm. We also compare the performance of these algorithms.