An important issue in designing wireless ad hoc and sensor networks is that of limited energy and bandwidth resources. Our focus throughout this paper is on energy efficiency. We are mainly concerned with a framework where it is more important to maximise the number of bits transmitted per joule of energy consumed than to maximise throughput. We use this framework to find an energy-efficient backbone network in wireless ad hoc and sensor networks. We also introduce an algorithm for designing two-tier ad hoc and sensor networks. To demonstrate the advantage of our new design method, we present simulation results comparing the effectiveness of our approach and previously proposed techniques.