Millimeter-wave communications is the most promising technology for next-generation cellular wireless systems, thanks to the large bandwidth available compared to sub-6 GHz networks. Nevertheless, communication at these frequencies requires narrow beams via massive MIMO and beamforming to overcome the strong signal attenuation, and thus precise beam-alignment between transmitter and receiver is needed. The resulting signaling overhead may become a severe impairment, especially in mobile networks with high users density. Therefore, it is imperative to optimize the beam-alignment protocol to minimize the signaling overhead. In this paper, the design of energy efficient joint beam-alignment protocols for two users is addressed, with the goal to minimize the power consumption during data transmission, subject to rate constraints for both users, under analog beamforming constraints. It is proved that a bisection search algorithm is optimal. Additionally, the optimal scheduling strategy of the two users in the data communication phase is optimized based on the outcome of beam-alignment, according to a time division multiplexing scheme. The numerical results show significant decrease in the power consumption for the proposed joint beam-alignment scheme compared to exhaustive search and a single-user beam-alignment scheme taking place separately for each user.