The invention relates to a pump comprising a dosage head (1) comprising a first part (2) and a second part (7) in which there is provided a hydraulic chamber (8) which is filled with a fluid and a dosage body (14) comprising means for driving a piston (13) of the pump in translation in the hydraulic chamber, a valve (17) for regularization of pressure in the hydraulic chamber, and at least one degassing path (33, 34, 36, 37) which extends in the second part, such that a first end of the path which forms the lowest point of the said path opens out at a junction between the piston and a seal fitted on the piston, and a second end of the path which forms the highest point of the said path opens out into a hollow body of the said valve.