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In a Wireless Sensor Network (WSN), energy saving is a key issue for prolonging its runtime. Usually, a real-time application of WSN requires that data be collected within a delay constraint. There exists a tradeoff between energy saving and delay satisfaction. In this paper, a Tree-based Energy and Delay Aware Scheme (TEDAS) is proposed, which is able to maximize the lifetime of WSN while delay bound is satisfied. Based on Expected Transmission Count (ETX) of link, the TEDAS initially creates the Minimum ETX Spanning Tree (MEST) of the WSN and then the MEST is gradually improved by the proposed Adjusting Tree Algorithm (ATA) so that the optimal data gathering tree is obtained. In addition, the lifetime optimization problem (LOP) is developed for the ATA to maximize network lifetime. Moreover, the complexity of the ATA is O(N3), where N is the number of the nodes in the WSN. Simulation results show that the proposed TEDAS outperforms some existing schemes in terms of network lifetime and the volume of valid data.