In this paper we evaluate the energy saving that can be achieved with the energy-aware cooperative management of the cellular access networks of two operators offering service over the same area. We evaluate the amount of energy that can be saved by using both networks in high traffic conditions, but switching off one of the two during the periods when traffic is so low that the desired quality of service can be obtained with just one network. When one of the two networks is off, its customers are allowed to roam over the one that is on. Several alternatives are studied, as regards the switch-off pattern: the one that balances the switch-off frequencies, the one that balances roaming costs, the one that balances energy savings, and the one that maximizes the amount of saved energy. Our results indicate that a huge amount of energy can be saved, and suggest that, to reduce energy consumption, new cooperative attitudes of the operators should be encouraged with appropriate incentives, or even enforced by regulation authorities.