A sucker rod pump with no travelling valve consisting of, from the bottom: hold down with pump inlet, lower standing valve, hollow coupling, upper standing valve suspended within the coupling, relief valve, hollow pump housing, solid piston within the housing, and barrel to clean and retain the piston in the housing. The piston attaches to and reciprocating with the rod string. Peripheral channels in the relief valve communicate between the coupling and the housing. A central channel in the relief valve communicates between the upper standing valve and the pump's outlets. The upstroke pulls fluid from the bottom of the well upward through the open lower standing valve, around the closed upper standing valve and into the housing chamber. The down stroke pushes fluid from the housing chamber past the closed lower standing valve and through the open upper standing valve to the pump's exit into the tubing.