Spontaneous nystagmus (SN) is a symptom of acute vestibular tone asymmetry. Alexander's Law (AL) states that slow-phase velocity of SN is higher when looking in the direction of fast-phases of nystagmus and lower in the slow-phase direction. Earlier explanations for AL predict that during SN, slow-phase eye velocity is a linear function of eye position, increasing linearly as eye deviates towards the fast-phase direction. Recent observations, however, show that this is often not the case; eye velocity does not vary linearly with eye position. Such new findings necessitate a re-evaluation of our understanding of AL. As AL may be an adaptive response of the vestibular system to peripheral lesions, understanding its mechanism could shed light on early adaptation strategies of the brain. Here, we propose a physiologically plausible mechanism for AL that explains recent experimental data. We use a dynamic control system model to simulate this mechanism and make testable predictions. This mechanism is based on the known effects of unilateral vestibular deficit on the response of the ipsi- and contralesional vestibular nuclei (VN) of the brainstem. This hypothesis is based on the silencing of the majority of ipsilesional VN units, which creates an asymmetry between the responses of the ipsi- and contralesional VN. Unlike former explanations, the new hypothesis does not rely on lesion detection strategies or signals originating in higher brain structures. The proposed model demonstrates possible consequences of acute peripheral deficits for the function of the velocity-to-position neural integrator of the ocular motor system and the vestibulo-ocular reflex.