A dispenser pump has a plunger operable in a body including an outer cylinder body having a vent opening in its sidewall and a body insert fitting into the top of the body cylinder and providing an external collar through which the plunger stem operates. The body insert has a lock-down thread to lock down the plunger for shipping. The insert also has an undulating annular vent-control bead extending right round its cylindrical outer surface, engaging the cylinder wall with interference for either blocking or unblocking the vent opening, according to whether the vent-control bead lies above or below the interior vent opening, by rotation between the body cylinder and body insert. The rotation can be driven by rotation of the plunger head, which makes a catch engagement with the top of the body insert. Blocking the vent during shipping reduces leakage.