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We consider a wireless sensor network where the nodes have limited energy. We first analyze the delay performance of a transmission scheme based on time division multiple access (TDMA). We propose a simple link scheduling algorithm to find the minimum-delay schedule given the slot lengths for all the links. We then combine these results with our previous work on energy-optimal cross-layer design to minimize the delay in transferring a fixed number of bits from the source nodes to the sink, in an energy-constrained manner. We also study the tradeoff between the total energy consumption and delay. Pareto optimal energy-delay curves are computed by solving a series of convex optimization problems where each objective function is a weighted sum of the delay and the total energy consumption. The computation is done for networks with and without link adaptation capabilities.