In vivo intracellular responses to auditory stimuli revealed that, in a particular population of cells of the ventral nucleus of the lateral lemniscus (VNLL) of rats, fast inhibition occurred before the first action potential. These experimental data were used to constrain a leaky integrate-and-fire (LIF) model of the neurons in this circuit. The post-synaptic potentials of the VNLL cell population were characterized using a method of triggered averaging. Analysis suggested that these inhibited VNLL cells produce action potentials in response to a particular magnitude of the rate of change of their membrane potential. The LIF model was modified to incorporate the VNLL cells' distinctive action potential production mechanism. The model was used to explore the response of the population of VNLL cells to simple speech-like sounds. These sounds consisted of a simple tone modulated by a saw tooth with exponential decays, similar to glottal pulses that are the repeated impulses seen in vocalizations. It was found that the harmonic component of the sound was enhanced in the VNLL cell population when compared to a population of auditory nerve fibers. This was because the broadband onset noise, also termed spectral splatter, was suppressed by the fast onset inhibition. This mechanism has the potential to greatly improve the clarity of the representation of the harmonic content of certain kinds of natural sounds.