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 at each single-antenna user. We show that the optimal beamforming strategies have an interesting nested zero-forcing structure. In the asymptotic regime where the number of antennas at each BS and that of users in each cell both grow large with their ratio tending to a finite constant, the dimensionality of the optimization problem that needs to be solved is greatly reduced, and only knowledge of statistics is required to solve it. The optimal solution is characterized in general, and an algorithm is proposed that converges to the optimal transmit parameters, for feasible SINR targets. For the two cell case, a simple single parameter characterization is obtained. These asymptotic results provide insights into the average performance, as well as simple but efficient beamforming strategies for the finite system case. In particular, the asymptotically optimal beamformers only require the BSs to have local instantaneous channel state information; the remaining parameters of the beamformers can be calculated using channel statistics, thereby reducing the channel state information estimation and signaling overhead.