Hydraulic circuits are typically controlled by throttling valves or variable displacement pump/motors. The first method throttles fluid for a desired pressure output and excess energy is lost through heat. While variable displacement pumps are more efficient, they are often large and expensive. An alternate method is the switch-mode control of hydraulic circuits through high-speed on-off valves. The proposed on-off valve design makes use of a continuously rotating disc to modulate flow between on and off states; the average power output or pulse duration is determined by the relative phase shift between the input and output ports. The addition of a directional valve to the the high-speed three-way valve allows any fixed displacement actuator to behave like a virtually variable displacement unit that is capable of four-quadrant control. In this paper a mathematical model focusing on the throttling, compressibility, internal leakage and viscous friction losses is developed and utilized to optimize the valve design for highest efficiency.