Recent physiological experiments have provided detailed descriptions of the properties of first-spike latency and variability in auditory cortex and nerve in response to pure tones with different envelopes. The envelope-dependence of first-spike timing and precision in auditory cortical neurons appears to reflect properties established in the nerve. First-spike latency properties in individual auditory nerve fibers are strongly correlated with their spontaneous rate (SR). It is shown here that a minimal, plausible model of auditory transduction with two free parameters accurately reproduces the physiological data from the auditory nerve population. The model consists of a simple gain stage, a bandpass filter, a rectifying saturating non-linearity, and a lowpass filter in series. The output of the lowpass filter drives an inhomogeneous Poisson process. The shape of the non-linearity is determined by SR; in physiological terms, this shape depends upon the resting sensitivity of the synapse between the inner hair cell and the auditory nerve. An alternative model for SR generation, where SR is added to the stimulus-driven output of a fixed nonlinearity, fails to account for the data. The results provide a novel, comprehensive and physiologically-based explanation for the range of experimental results on the envelope-dependence of first-spike latency and precision, and its relationship with SR, in the auditory system.