In this study, the potential of reducing radio base station operational energy consumption is discussed in terms of deploying sleep modes. By periodically switching off the base station transmission, or using fewer transmit antennas, the energy consumption of base station hardware decreases. By delivering less control signalling overhead, the radio frequency energy consumption can also be reduced. Taking the long-term evolution system as an example, up to 90% radiated energy reduction can be obtained in low traffic conditions by employing time-domain optimisation in each radio frame. The optimum on/off duty cycle is derived, enabling the energy consumption of the base station to scale with traffic load. In the spatial domain, an antenna selection criterion is proposed, indicating the most energy-efficient antenna configuration as a function of users' locations and quality of service requirements. Without time-domain sleep modes, using fewer transmitter antennas could outperform full antenna transmission. However, with time-domain sleep modes, using all available antennas is generally the most energy-efficient choice.