Response of a variable frequency switching constant on-time or adaptive on-time controlled power converter to a large step-up or step-down change in load is improved with a simple circuit that detects magnitude and polarity of a change in output voltage and initiates, extends or terminates conduction of power pulses from an input source through said power converter. Both the amplitude and duration of undershoot or overshoot of the transient response are reduced or, alternatively, the capacitance of an output filter may be significantly reduced and still provide comparable transient performance. The fast adaptive on-time control is applicable to multi-phase power converters using phase managers or one or more phase-locked loops for interleaving of power pulses.