A wireless sensor network (WSN) comprises a large number of wireless sensor nodes. Wireless sensor nodes are battery-powered devices with limited processing and transmission power. Therefore, energy consumption is a critical issue in system designs of WSNs. In-network data fusion and clustering have been shown to be effective techniques in reducing energy consumption in WSNs. However, clustering can introduce bottlenecks to a network, which causes extra delays in a data aggregation process. The problem will be more severe when in-network data fusion does not yield any size reduction in outgoing data. Such problems can be greatly alleviated by modifying the network structure. In this paper, a delay-aware network structure for WSNs with in-network data fusion is proposed. The proposed structure organizes sensor nodes into clusters of different sizes so that each cluster can communicate with the fusion center in an interleaved manner. An optimization process is proposed to optimize intra-cluster communication distance. Simulation results show that, when compared with other existing aggregation structures, the proposed network structure can reduce delays in data aggregation processes and keep the total energy consumption at low levels provided that data are only partially fusible.