An adjustable rotary vane pump configured to reduce pressure pulsations during hydraulic fluid discharge includes a housing having two side plates positioned in parallel. Each side plate has multiple grooves formed in its surface. A rotor mounted between the side plates has multiple vanes extending radially outward. A lift ring surrounds the rotor, pivotally connected to the housing to swivel between positions eccentric to the housing. During rotation of the rotors, the vanes divide the annular region between the rotor and the lift ring into multiple cells, which alternately position themselves between a suction zone and a pressure zone of the pump. In a transition region between the suction and pressure zone, when the lift ring is between pre-determined angular positions, the grooves within lift ring and the side plate substantially align to create an overflow channel, which transfers the hydraulic fluid from the suction zone to the pressure zone.