We define a transmission power adaptation-based routing technique that finds optimal paths for minimum energy reliable data transfer in multi-hop wireless networks. This optimal choice of the transmission power depends on the link distance between the two nodes and the channel characteristics. Typical energy efficient routing techniques use a transmission power such that the received signal power at the destination minimally exceeds a desired threshold signal strength level. In this paper we argue that such a choice of the transmission power does not always lead to optimal energy routes, since it does not consider differences in the receiver noise levels. We first analyze the optimal transmission power choices for both the ideal case from an information-theoretic perspective, and for realistic modulation schemes. Subsequently we define our technique for transmission power adaptation that can be used in existing routing protocols for multi-hop wireless networks. Our simulations show that current best-known schemes incur upto 10% more energy costs in low noise environments, and upto 165% more energy costs in high noise environments compared to our proposed scheme.