A power converter using constant on-time (COT) or ramp pulse modulation (RPM) control achieves more rapid resumption of steady-state operation after a step-up load transient by extending an on-time of a switching pulse by interrupting a ramp voltage waveform that is compared with a threshold that equals a threshold voltage at the termination of a switching pulse or increasing a voltage with which the ramp voltage is compared. These techniques are applied to both single-phase and multi-phase power converters.