A fixed-nozzle dispenser pump suitable for large doses has a downwardly-directed nozzle tip (32) and an outlet valve arrangement (4) in a nozzle (3). A blocking element, such as a ball (41), of the outlet valve arrangement (4) is biased back along a close-fitting tubular draw path (43) in the valve after dispensing, so as to draw product back out of the nozzle tip and prevent dripping. A further feature is a subdivision of the nozzle tip and a flexible flap valve (35) blocking a resulting passage segment in the nozzle. This facilitates clearance of another nozzle passage (36) by the reverse suction. A further feature is a membrane (24) across the front of the piston plunger, advanceable relative to a piston seal (231) by pressure of a plunger head (21). This helps accomomodate the returned fluid and enables a spot-dosing action.