Abstract: High efficiency, high pressure fixed displacement pump systems and methods of control. A typical application is for engine driven high pressure pumps for powering loads such as fuel injectors and/or hydraulic engine valve actuators. The pump systems include a control valve controllably coupling the pump output back to the pump input to stop the pumping when the desired pressure of the output is reached. Reinitiating pumping an increment in crankshaft angle before a load event based in the increment in pressure needed to reach the desired pressure at the crankshaft angle of the load event provides a simple control algorithm assuring accurate repeatability in the pressure at the beginning of a load event. Pumping throughout the load event minimizes the decrease in pressure during the load event. Providing underlap in the control valve minimizes pressure peaks and maximizes efficiently when starting and stopping the pumping action. Various embodiments are disclosed.