A pressure limiter and pump for use in a testing string. The pressure limiter has an outer case and an inner mandrel which form an enclosure defining an annulus therebetween. The inlet and outlet check valves in the annulus define a pumping chamber therebetween which opens toward the pump. Fluid in the pumping chamber is never vented to the well annulus. In a first embodiment, a transversely mounted pressure limiter piston provides communication between the pumping chamber and a lower portion of the testing string when actuated. In the second and third embodiments, a pressure limiter piston is reciprocably disposed in the annulus between the case and mandrel; at a predetermined pressure differential, the pressure limiter piston reciprocates such that the volume in the pumping chamber is increased. A fourth embodiment simply uses a pumping chamber of predetermined volume such that the efficiency of the pump drops to essentially zero when the pressure in the pumping chamber reaches a predetermined level; no pressure limiter piston is used.