A method of controlling the respective transmit powers allocated by a base station of a cellular communications network to each of a plurality of sub-bands is provided. Information from at least one other base station of the network is received, the information comprising information about a sensitivity of a utility function in a cell served by the other base station to changes in powers allocated to respective sub-bands by the base station. A sub-band is identified in which it would be relatively advantageous to increase a transmit power. It is determined whether a factor relating to a happiness of users in the cell exceeds a threshold value. The transmit power in the identified sub-band is increased only if the happiness factor is less than the threshold value.