Masked detection threshold for a short tone in noise improves as the tone's onset is delayed from the masker's onset. This improvement, known as "overshoot," is maximal at mid-masker levels and is reduced by temporary and permanent cochlear hearing loss. Computational modeling was used in the present study to evaluate proposed physiological mechanisms of overshoot, including classic firing rate adaptation and medial olivocochlear (MOC) feedback, for both normal hearing and cochlear hearing loss conditions. These theories were tested using an established model of the auditory periphery and signal detection theory techniques. The influence of several analysis variables on predicted tone-pip detection in broadband noise was evaluated, including: auditory nerve fiber spontaneousrate (SR) pooling, range of characteristic frequencies, number of synapses per characteristic frequency, analysis window duration, and detection rule. The results revealed that overshoot similar to perceptual data in terms of both magnitude and level dependence could be predicted when the effects of MOC efferent feedback were included in the auditory nerve model. Conversely, simulations without MOC feedback effects never produced overshoot despite the model's ability to account for classic firing rate adaptation and dynamic range adaptation in auditory nerve responses. Cochlear hearing loss was predicted to reduce the size of overshoot only for model versions that included the effects of MOC efferent feedback. These findings suggest that overshoot in normal and hearing-impaired listeners is mediated by some form of dynamic range adaptation other than what is observed in the auditory nerve of anesthetized animals. Mechanisms for this adaptation may occur at several levels along the auditory pathway. Among these mechanisms, the MOC reflex may play a leading role.