A computing device-controlled system is described for the generation of amplitude-modulated pulse-width modulation (AMPWM) signals for use in treating neurological dysfunction via cranial neurostimulation, where the AMPWM signal is specifically designed to minimize the electrical impedance of the tissues of the head. A low-frequency carrier signal is determined for the AMPWM signal by measuring EEG activity at a reference site or sites, generally corresponding with the location of suspected brain dysfunction. Carrier signal frequency is variably related to critical frequency components of the EEG power spectral density, determined from statistical analysis of amplitudes and variability, and dynamically changed as a function of time to prevent entrainment. The AMPWM signal is presented to a subject via a plurality of neurostimulation delivery modes for therapeutic use.