Sleep modes are emerging as a promising technique for energy-efficient networking: by adequately putting to sleep and waking up network resources according to traffic demands, a proportionality between energy consumption and network utilization can be approached, with important reductions in energy consumption. Previous studies have investigated and evaluated sleep modes for wireless access networks, computing variable percentages of energy savings. In this paper we characterize the maximum energy saving that can be achieved in a cellular wireless access network under a given performance constraint. In particular, our approach allows the derivation of realistic estimates of the energy-optimal density of base stations corresponding to a given user density, under a fixed performance constraint. Our results allow different proposals to be measured against the maximum theoretically achievable improvement. We show, through numerical evaluation and simulation, the possible energy savings in today's networks, and we further demonstrate that even with the development of highly energy-efficient hardware, a holistic approach incorporating system level techniques is essential to achieving maximum energy efficiency.