The authors propose an adaptive cell-breathing (ACB) technique to improve the energy efficiency (EE) of a downlink cellular network consisting of small-cell base stations (BSs), wherein each BS adaptively adjusts its transmission power such that the received signal strength of the worst-case user is larger than a pre-defined threshold. They also propose an aggressive BS on-off (ABO) technique in which the small-cell BSs having a number of users smaller than a certain value, N th , are turned off, whereas conventional techniques only turn off the empty BSs. They adopt a stochastic geometry for modelling the locations of both BSs and users. Simulation results show that the ACB technique yields a much better EE than the power on-off technique with a fixed power, including the ABO technique. In particular, the EE of the ACB technique is proportional to (λ b) c (c > 0), where λ b denotes the BS density and the exponent c denotes the increasing ratio of the EE to λ b in the log − log domain. The EE of the ABO technique tends to increase as N th increases.