Irrigation fluid is aspirated from an eye and through an aspiration instrument by operating a vacuum pump, including moving first and second plungers between respective suction strokes and discharge strokes. Vacuum pressure at an input side of the pump is maintained at a desired vacuum pressure setting by controlling speeds and directions of the plungers, and controlling positions of input and output valves communicating with cylinders in which the plungers move. Controlling is based on the pressure setting and measured pressures in the cylinders. Vacuum pressure is maintained while transitioning from the suction stroke of the first plunger to the suction stroke of the second plunger, by synchronizing respective positions of the plungers and the valves, such that initiation of the suction stroke of the second plunger during the transitioning is delayed until a vacuum pressure in the second cylinder is equal to a vacuum pressure in the first cylinder.
