As wireless networks evolve to deal with increasing traffic demand and an increasing number of users, energy efficiency is becoming increasingly important. Area power consumption, defined as the ratio of total radio access network power consumption to the area covered, is a key metric for comparing the energy efficiency of different network designs. This paper examines the optimization of an LTE type cell for energy efficiency by minimizing the area power consumption (APC) subject to user coverage and capacity constraints. First we show that operating the base station at the maximum transmit power (and cell size) which services all users optimizes APC. Next we show that APC is optimum when the base station operates with the minimum bandwidth necessary to service all users. Finally we show that a modified admission scheme (which increases the minimum SINR at which a user will be serviced) improves APC by increasing the maximum capacity and size of cells that can be supported. In addition to improving energy efficiency, the modified scheme requires fewer cells in new or overlay deployments and may potentially permit removal of cells from an existing network.