The invention relates to a pump with a membrane and hydraulic control, comprising a pumping chamber (3) provided between a head and a pump body (9), with a mobile wall consisting of a membrane that is elastically deformable from the rest shape thereof corresponding to the state thereof at the end of the suction stroke of the pump, an intermediate hydraulic chamber (8) having a constant space provided in the pump body (9) and comprising a piston (10) capable of a reciprocating movement inside said intermediate chamber (8), a leak compensation space of the intermediate chamber (8) connected to the latter by a feedback channel (28, 21, 18) via a free load-free one-way valve (13) ensuring a flow towards the working chamber (8), characterised in that the one-way valve (13) and at least a portion (34) of the compensation space are contained in a body (22, 31) added onto the pump body (9); at the highest point of the intermediate hydraulic chamber (8) in the working position of the pump.