Changes in the temporal envelope are important defining features of natural acoustic signals. Many cells in the inferior colliculus (IC) respond preferentially to certain modulation frequencies, but how they accomplish this is not yet clear. We therefore made whole-cell patch-clamp recordings in the IC of anesthetized mice while presenting sinusoidal amplitude-modulated (SAM) tones. The relation between the number of evoked spikes and modulation frequency was used to construct rate modulation transfer functions (rMTFs). We observed different types of rate tuning, including band-pass (16%), band-reject (13%), high-pass (6%) and low-pass (6%) tuning. In the high-pass rMTF neurons and some of the low-pass rMTF neurons, the tuning characteristics appeared to be already present in the inputs. In both band-pass and band-reject rMTF neurons, the non-linear relation between membrane potential and spike probability ensured preferential spiking during only a small part of the modulation period. Band-pass rMTF neurons had rapidly rising EPSPs, allowing good phase-locking to brief tones and intermediate modulation frequencies. At low modulation frequencies, adaptation of their spike threshold contributed to the onset response. In contrast, band-reject rMTF neurons responded with small EPSPs or IPSPs to brief tones. In these cells, a power law could describe the supra-linear relation between average membrane potential and spike rate. Differences in timing of synaptic input and presence or absence of spike adaptation therefore define band-pass and band-reject rate tuning to SAM tones in the mouse IC.