A rod-drawn pump for use in a well includes a tubing and a rod reciprocating within the tubing to move a plunger in a series of alternating upward strokes and downward strokes. The plunger defines a pump chamber with a standing valve through which liquid from the well passes during the upward stroke of the plunger. During the downward stroke, the liquid in the pump chamber passes through a traveling valve in the plunger and into a particular cavity defined by the plunger and a third valve. During the next upward stroke, the liquid in the particular cavity passes through the third valve to produce a column of the liquid which is eventually lifted from the well. The third valve supports the column of the liquid during the next downward stroke so that the traveling valve in the plunger is open when it contacts the surface of the liquid in the pump chamber. This inhibits gas and liquid pound during the downward stroke. Portions of the rod at least partially define a passage which bypasses the third valve near the end of the downward stroke to substantially fill the particular cavity prior to the upward stroke. This inhibits any gas or liquid pound which might otherwise result during the upward stroke.