A pump controller has a signal processor that receives signaling about an instant water level AIL of a liquid in a container and generated by a water level transducer during an empty/fill application; and determines corresponding signaling to control a pump during the empty/fill application based upon the signaling received using a liquid level control algorithm that turns ON the pump when the instant water level AIL rises above a maximum empty water level during an empty application, or falls below a maximum fill water level during a fill application; turns OFF the pump when the instant water level AIL falls below a minimum empty water level for the empty application, or rises above a second maximum fill water level during the fill application; controls the pump when the instant water level AIL is in a liquid level region above the minimum empty water level and below a second maximum empty water level for the empty application, or falls below the second maximum fill water level and above a second minimum fill water level during the fill application based upon a respective desired adaptive pressure set point SP* being defined from a respective adaptive liquid level control curve with respect to the instant water level AIL.