The thermodynamic cycle appropriate to an AMTEC (alkali metal thermal-to-electric converter) cell is discussed for both liquid- and vapor-fed modes of operation, under the assumption that all processes can be performed reversibly. In the liquid-fed mode, the reversible efficiency is greater than 89.6% of Carnot efficiency for heat input and rejection temperatures (900-1300 K and 400-800 K, respectively) typical of practical devices. Vapor-fed cells can approach the efficiency of liquid-fed cells. Quantitative estimates confirm that the efficiency is insensitive to either the work required to pressurize the sodium liquid or the details of the state changes associated with cooling the low pressure sodium gas to the heat rejection temperature.