In this work we study the dynamic one-to-one communica- tion problem in energy- and capacity-constrained wireless ad-hoc net- works. The performance of such networks is evaluated under random traffic generation and continuous energy recharging at the nodes over an infinite-time horizon.We are interested in the maximum throughput that can be sustained by the network with the node queues being finite and in the average packet delay for a given throughput. We propose a multicost energy-aware routing algorithm and compare its performance to that of minimum-hop routing. The results of our experiments show that gener- ally the energy-aware algorithm achieves a higher maximum throughput than the minimum-hop algorithm. More specifically, when the network is mainly energy-constrained and for the 2-dimensional topology consid- ered, the throughput of the proposed energy-aware routing algorithm is found to be almost twice that of the minimum-hop algorithm.