In this work, we propose an energy-efficient multicasting 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 multicasting, taking into account: i) the node residual energies, ii) the transmission powers used by the nodes, and iii) the set of nodes covered. Our algorithm is optimal, in the sense that it can optimize any desired function of the total power consumed by the multicasting 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 optimal algorithm has non-polynomial complexity, thus, we propose a relaxation producing a near-optimal solution in polynomial time. The performance results obtained show that the proposed algorithms outperform established solutions for energy-aware multicasting, 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.