An explanation of the existence of the plateau of emission from 3.4 to 3.6-mu-m and the weak peaks at 3.46, 3.51 and 3.56-mu-m in the unidentified infrared emission features is presented in terms of the vibrational transitions of the fulleranes and their ions. It is suggested that the 3.46-mu-m peak is attributable to aliphatic C-H stretching shifted from the usual wavelength of 3.40-mu-m by the effect of a vacant site (i.e. a missing hydrogen atom) at one of the neighbouring carbon atoms. Two neighbouring vacant sites have a greater effect and shift the wavelength to give rise to the 3.51-mu-m line, and three produce the 3.56-mu-m line. The existence of three peaks is thus a simple consequence of each carbon atom in the fulleranes having three other carbon atoms as nearest neighbours. More distant vacant sites shift these peaks in the same way but to a lesser extent, and the plateau is explained as the blending of a large number of peaks shifted by different amounts. A few anomalous sources are known, such as HD 97048, whose spectrum is dominated by two emission peaks at wavelengths different from the above, one at 3.43-mu-m and a stronger one at 3.53-mu-m. It is shown that fulleranes with highly symmetrical arrangements of hydrogen atoms can give rise to strong peaks in the spectrum, and a tetrahedral isomer of C60H36 is exhibited with a spectrum, calculated from the present model, which bears a resemblance to that of HD 97048; it seems to be identical to an isomer which has been synthesized in the laboratory.