This paper considers base station (BS) cooperation in the form of coordinated beamforming, focusing on min-max fairness in the power usage subject to target SINR constraints. We show that the optimal beamforming strategies have an interesting nested zero-forcing structure. We then consider the asymptotic regime where the number of antennas at each BS and the number of users in each cell both grow large with their ratio tending to a finite constant. The limiting optimal beamformer structure is characterized in terms of the solution of a convex optimization problem. The dimensionality of this optimization problem is constant1, as opposed to the problem of solving for the exactly optimal beamformer2, and only knowledge of statistics is required to solve it. These asymptotic results provide insights into the average performance, as well as simple but efficient strategies for the finite system case. In particular, the optimal beamforming strategy from the large systems analysis only requires the base stations to have local instantaneous channel state information; the remaining parameters of the beamformer can be calculated using channel statistics which can easily be shared amongst the base stations.