Summary form only given. We consider the problem of broadcasting messages in a wireless energy-limited network so as to maximize network lifetime. An O(e log e) algorithm to construct a broadcast tree that maximizes the critical energy of the network following the broadcast is developed. Additionally, we propose two new greedy heuristics to construct minimum energy broadcast trees. We show how our maximum critical energy algorithm may be coupled with our proposed greedy heuristics as well as with the greedy heuristics proposed earlier in the literature for the construction of minimum energy broadcast trees. Extensive simulations performed by us show that this coupling improves network lifetime significantly (between 48.3% and 328.9%) when compared with network lifetime using the base greedy heuristics in isolation.