The focus of this work is on cost and complexity- induced rank-constrained precoding for millimeter- wave (mmW) multi-input multi-output (MIMO) systems. The higher antenna dimensionality and sparse channel structure of mmW systems motivate directional precoding schemes over more complex and less robust eigen-mode-based precoding schemes. Building on a prior work that illustrated the superiority in design, robustness and performance of a directional rank-1 beamformer, this work considers higher-rank directional precoding structures for mmW systems. It is shown that directional precoders continue to enjoy similar properties in single-user MIMO (SU-MIMO) systems. But from a network efficiency consideration, it would be more worthwhile to expend the radio frequency (RF) chain resource on multi-user transmissions. Towards this goal, a directional scheduler and different directional beamforming structures are proposed here. These structures are shown to result in significant performance improvement over higher-rank SU-MIMO schemes.