In this paper we propose an energy-efficient broadcast algorithm for wireless networks for the case where the transmission powers of the nodes are fixed. Our algorithm is based on the multicost approach and selects an optimal energy-efficient set of nodes for broadcasting, taking into account: i) the node residual energies, ii) the transmission powers used by the nodes, and iii) the set of nodes that are covered by a specific schedule. Our algorithm is optimal, in the sense that it can optimize any desired function of the total power consumed by the broadcasting task and the minimum of the current residual energies of the nodes, provided that the optimization function is monotonic in each of these parameters. Our algorithm has non-polynomial complexity, thus, we propose a relaxation producing a near-optimal solution in polynomial time. Using simulations we show that the proposed algorithms outperform other established solutions for energy-aware broadcasting with respect to both energy consumption and network lifetime. Moreover, it is shown that the near-optimal multicost algorithm obtains most of the performance benefits of the optimal multicost algorithm at a smaller computational overhead.