Natural sounds, especially communication sounds, have highly structured amplitude and phase spectra. We have quantified how structure in the amplitude spectrum of natural sounds affects coding in primary auditory afferents. Auditory afferents encode stimuli with naturalistic amplitude spectra dramatically better than broad-band stimuli (approximating white noise); the rate at which the spike train carries information about the stimulus is 2-6 times higher for naturalistic sounds. Furthermore, the information rates can reach 90% of the fundamental limit to information transmission set by the statistics of the spike response. These results indicate that the coding strategy of the auditory nerve is matched to the structure of natural sounds; this `tuning' allows afferent spike trains to provide higher processing centres with a more complete description of the sensory world.