Pump for dispensing a dose of a fluid product, comprising a tubular body including an intake orifice; an end member associated with the body and including a rest abutment and an end-of-stroke abutment; a compression member mounted so as to move inside the body between a rest position in which said compression member is in abutment against the rest abutment, and an end-of-stroke position in which said compression member is in abutment against the end-of-stroke abutment, said compression member being elastically returned toward the rest position and including an exhaust orifice; a metering chamber; and an intake valve and an exhaust valve adapted to selectively close off the intake orifice and the exhaust orifice, respectively.