Absence of line power supplies imposes severe constraints on nodes in wireless ad hoc and sensor networks. In this paper, we concentrate on finding a broadcast tree that maximizes the network's lifetime. Previous studies showed that this problem is polynomially solvable when assuming receivers consume no energy or only designated receivers consume energy for receiving packets. Due to the broadcast nature of the wireless medium, however, unintended active nodes in the receiving range of a transmitting node may overhear the message and hence contribute to energy wastage. Under the overhearing cost (OC) model, the problem becomes NP-hard and the approximation ratio of the existing solutions, which are optimal under the non-overhearing cost (NOC) model, can be as bad as ω(n). We investigate the problem by developing heuristic solutions. Simulation results show that our algorithms outperform the existing ones by up to 100%.