In traditional approaches to energy efficient routing, a node needs to receive routing messages from all of its neighbors to be able to select the best route. In a previous work, we have proposed a technique that enables the best route selection based on exactly one message reception [1]. Our protocol delays forwarding of routing messages (RREQ) for an interval inversely proportional to the residual energy. Energy-delay mapping techniques make it possible to enhance an existing min-delay routing protocol into an energy-aware routing that maximizes the lifetime of sensor networks. We have proposed some heuristic functions to perform the energy-delay mapping. This paper analyzes their limitations and derives a suitable synthetic function that guarantees that a node selects the best route with very high probability. We also identify comparative elements that help us to perform a thorough a posteriori comparison of the mapping functions in terms of the route selection precision. Simulation results show that our synthetic functions select routes with very high precision while keeping the propagation delay of routing messages reasonable.