Data gathering is a broad research area in wireless sensor networks. The basic operation in sensor networks is the systematic gathering and transmission of sensed data to a sink for further processing. The lifetime of the network is defined as the time until the first node depletes its energy. A key challenge in data gathering without aggregation is to conserve the energy consumption among nodes so as to maximize the network lifetime. We formalize the problem of tackling the challenge as to construct a min-max-weight spanning tree, in which the bottleneck nodes have the least number of descendants according to their energy. However, the problem is NP-complete. A ??(log n/log/log n)-approximation algorithm MITT is proposed to solve the problem without location information. Simulation results show that MITT can achieve longer network lifetime than existing algorithms.