A theory is investigated in which the carriers of the diffuse interstellar bands are fullerane molecules and their ions, such as the series C60Hm, m=1, 2,...,60. No suitable spectra are available for these molecules, so certain small hydrocarbons are studied instead which have electronic systems similar to those found in some of the fulleranes. The properties of these analogues are reviewed and assessed, not only for the presence of transitions at wavelengths close to those of interstellar features, but also for the absence of transitions at wavelengths where no interstellar features are known, and the allyl radical C3H5 is found to be worthy of note. It has a transition whose origin is at 4083 Å, not far from the diffuse band at 4430 Å, and another close to the interstellar absorption feature at 2175 Å. The visible transition is weak, but is nevertheless strong enough that allyl radicals embedded in the surfaces of fulleranes might carry λ4430 if the interstellar abundance is high, in which case they would also be responsible for a few per cent of the intensity of λ2175. A weak correlation would then be expected between λλ2175 and 4430 Å, but a strong one is known, and this fact leads to an investigation of the carrier of λ2175. No specific identification is suggested, but the strength of this and other correlations may be explained if λ2175 is itself a transition of some small system of π-electrons embedded in the fulleranes.