Cooperative geographic routing has emerged as an efficient, scalable routing paradigm that exploits the joint merit of cooperative diversity and position-aided localized operation to enhance the network performance. In terms of the hop efficiency, an existing scheme called Relay-Aware Cooperative Routing (RACR) has offered a cross-layer approach based on its quantitative study of how physical-layer cooperation leads to link-layer radio coverage extension, under the policy of equal power allocation (EPA) over the cooperating nodes. However, the effect of cooperation-based radio coverage extension dramatically varies with the power allocation policy in use. In this paper, we extend the RACR scheme by addressing a power-optimized cooperative geographic routing problem. With the joint optimization of relaying position and power allocation, the maximum cooperative transmission range is derived. We then, according to the result, present a modified cross-layer routing protocol taking into account the effectuation of optimal power allocation (OPA). Simulation results show that the proposed scheme effectively improves the coverage extension performance as well as reduces the average number of hops.