In this paper we investigate the use of wired short cuts in sensor networks. This new paradigm augments a sensor network with a very limited wired infrastructure to improve its overall energy-efficiency. Energy-efficiency is obtained by reduction in average path length. We have developed an analytical model to analyze the gain in path length reduction by using short cuts. We have also conducted extensive simulations to validate our analysis. Our results show that there is an optimal wire length for which the path length reduction is at its maximum, beyond which it decreases. The optimal length is only a small fraction (37.8-50%) of the network diameter. In a network with 1000 nodes uniformly distributed on a disk the path length reduction saturates at 60-70% with 5-24 wires, depending on the location of the sink. Also, we find that restricting the knowledge about the wires to 2 hops does not degrade the performance from the case when we have global knowledge of all wires. These results show promise of the new paradigm.