The nature of wireless sensor networks make them suitable for a great variety of applications, especially over wide areas, or in remote or hostile locations; however, such environments make battery capacity an especially important concern, where replacing or recharging of batteries is infeasible for one reason or another. Battery capacity restrictions on highly energy-constrained sensor networks can be mitigated, by adopting data-aggregation techniques and by managing the scheduling of nodes. These effectively reduce the overall amount of data transmitted, thereby conserving energy. In this paper, we address the construction of energy-efficient data-aggregation trees, an NP-problem, in different rounds of communication, seeking to maximize the lifetime of heterogeneous sensor networks. This problem is subject to constraints on such networks: battery capacity, data-sensing scheduling, and round calculation. We derive a near-optimal primal feasible solution using Lagrangean Relaxation. The experimental results show that our proposed algorithm outperforms similar algorithms.