Due to the limited energy supplies of nodes in many applications like wireless sensor networks, energy efficiency is crucial for extending the lifetime of these networks. This paper addresses the routing problem for outage-restricted multihop wireless ad hoc networks based on cooperative transmission. The source node wants to transmit messages to a single destination. Other nodes in the network may operate as relay nodes. In this paper, a new cooperative routing protocol is introduced using the Alamouti space-time code for the purpose of energy savings, given a required outage probability at the destination. Two efficient power allocation schemes are derived, which depend only on the statistics of the channels. In the first scheme, each node needs to know only the local channel statistics, and can be implemented in a distributed manner. In the second scheme, a centralized power control strategy is proposed, which has a higher energy efficiency, at the expense of more complexity and signalling overhead. Compared to non-cooperative multihop routing, an energy saving of 80% is achievable in line networks with 3 relays and an outage probability constraint of 10-3 at the destination.