A method of cleaning out blockages which prevent operation of a reciprocating downhole tubing pump. A first step involves mechanically displacing and disabling, without removing, a ball from a ball seat on the travelling ball valve. A second step involves mechanically displacing and disabling, without removing, a ball from a ball seat on the standing valve assembly. A third step involves inserting coil tubing through the travelling ball valve and the standing ball valve to cleanout the entire workstring and pump.