A system and method for controlling the speed of a progressing cavity liquid well pump to increase liquid production from a well while avoiding operation of the well in a pumped-off state. A controller controls a variable speed drive to drive a progressing cavity liquid well pump at a set pump speed while measuring well and system parameters indicative of pumping performance and/or liquid production from the well. The set speed of the pump is changed in steps either increasingly or decreasingly by the controller, acting through the variable speed drive, in response to the measured well and system parameters. The controller, responsive to the measured well and system parameters, challenges the set pump speed by varying the set pump speed so as to increase the production from the well while avoiding pump and well operation in a pumped-off state.