A hard disk drive or other disk-based storage device comprises a storage disk, a write head configured to write data to the disk, and control circuitry coupled to the write head. The control circuitry comprises a write driver and degauss circuitry associated with the write driver. The degauss circuitry is configured to control a degauss signal waveform to be applied to the write head by the write driver, and comprises separate amplitude envelope control mechanisms for steady state and overshoot portions of the degauss signal waveform. The separate amplitude envelope control mechanisms may comprise, for example, separate steady state and overshoot controllers for controlling the amplitude envelope decay rates of the respective steady state and overshoot portions of the degauss signal waveform over the plurality of pulses.