Human detection thresholds in tone-in-noise (TIN) paradigms cannot be explained by the prevalent power-spectrum model when stimulus energy is made less reliable, e.g., in roving-level or equal-energy paradigms. Envelope-related cues provide an alternative that is more robust across level. The TIN stimulus envelope is encoded by slow fluctuations in auditory-nerve (AN) responses - a temporal representation affected by inner-hair-cell (IHC) saturation and cochlear compression. Here, envelope-related fluctuations in AN responses were hypothesized to be reflected in responses of neurons in the inferior colliculus (IC), which have average discharge rates that are sensitive to amplitude-modulation (AM) depth and frequency. Responses to tones masked by narrowband gaussian noise (GN) and low-noise noise (LNN) were recorded in the IC of awake rabbits. Fluctuation amplitudes in the stimulus envelope and in model AN responses decrease for GN maskers and increase for LNN upon addition of tones near threshold. Response rates of IC neurons that are excited by AM were expected to be positively correlated with fluctuation amplitudes, whereas rates of neurons suppressed by AM were expected to be negatively correlated. Of neurons with measurable TIN-detection thresholds, most had the predicted changes in rate with increasing tone level for both GN and LNN maskers. Changes in rate with tone level were correlated with envelope sensitivity measured with two methods, including the maximum slopes of modulation transfer functions. IC rate-based thresholds were broadly consistent with published human and rabbit behavioral data. These results highlight the importance of midbrain sensitivity to envelope cues, as represented in peripheral neural fluctuations, for detection of signals in noise.