The diagrid structural system has widely been used for tall buildings due to its structural efficiency and distinctive architectural aesthetic potentials. This paper extends the previous studies on diagrids by further investigating more efficient diagrid configurations which require less amount of structural material to meet design requirements. Today, sustainable design to save our limited resources is one of the most important building design issues, especially for tall buildings constructed with an abundant amount of resources. Diagrid structures of uniform and various varying angle configurations are studied to determine more efficient geometric configurations of the system.