A dispenser having a fluid reservoir (R) and a dispenser member (D) mounted on the reservoir (R), the reservoir (R) forming a cylinder (11) and including a piston (2; 2′) that slides in the cylinder (11) so as to decrease the working volume of the reservoir (R). The leaktight slide cylinder (11) contains a separator element (3a) that divides the reservoir into two compartments (Ri, Rs), namely a lower compartment (Ri) that is defined between the piston (2; 2′) and the separator element (3a), and an upper compartment (Rs) that is defined between the separator element (3a) and the dispenser member (D). The separator element (3a) includes at least one through hole (33) that puts the two compartments (Ri, Rs) into communication with each other, the separator element moving in the leaktight slide cylinder in response to the dispenser member being actuated by pressing on the pusher.