The achievable gains via power-optimal scheduling are investigated. Under the QoS constraint of a guaranteed link rate, the overall power consumed by a cellular BS is minimized. Available alternatives for the minimization of transmit power consumption are presented. The transmit power is derived for the two-user downlink situation. The analysis is extended to incorporate a BS power model (which maps transmit power to supply power consumption) and the use of DTX in a BS. Overall potential gains are evaluated by comparison of a conventional SOTA BS with one that employs DTX exclusively, a power control scheme and an optimal combined DTX and power control scheme. Fundamental limits of the achievable savings are found to be at 5.5 dB under low load and 2 dB under high load when comparing the SOTA consumption with optimal allocation under the chosen power model.