A Coordinated Multipoint (CoMP) controller advantageously reduces the transmit powers of transmissions coordinated across a plurality of sub-cells within a CoMP cell. The CoMP controller determines serving sub-cell path gains and interfering sub-cell path gains for a set of mobile terminals to be served by distinct sub-cells. The CoMP controller then evaluates an objective function that expresses an aggregate throughput of concurrent transmissions to be sent to or received from the set of mobile terminals as a function of the serving sub-cell path gains, the interfering sub-cell path gains, and the individual transmit powers of those transmissions, to determine the combination of individual transmit powers that maximizes the aggregate throughput while meeting minimum quality of service requirements for the mobile terminals. The combination of individual transmit powers will necessarily require less power than if the concurrent transmissions were each sent at maximum transmit power.