<p>A variable-eccentricity vane pump (1) having a rotor (5) fitted with blades; an adjusting ring (4) housing the rotor (5); elastic means (6) for forcing the adjusting ring (4) into a maximum-eccentricity position with respect to the rotor (5) ; a first sliding member (12) connected to the adjusting ring (4) and which slides in fluidtight manner inside a first chamber (9) connected hydraulically to a delivery conduit of the pump; and a second sliding member (13) connected to the adjusting ring (4) and which slides in fluidtight manner inside a second chamber (10) connected hydraulically to a delivery conduit of the pump. The first sliding member (12) is connected to the adjusting ring (4) on the opposite side to the elastic means (6) and the second sliding member (13) ; and the second chamber (10) is smaller than the first chamber (9) , and has a drain opening (11) formed in a lateral wall (10a) on which the second sliding member (13) slides.</p>