A theory in which the diffuse interstellar bands are carried by the fulleranes C 60 H m (m = 1,2,..., 60) and their ions is investigated further. The molecules of this series have a variety of π-electron systems which are here assigned to two categories by size: global systems, which involve most of the carbon atoms in the molecule, and local systems, which involve only a few. Known differences in the spatial distribution of interstellar bands of different width then suggest that the narrow bands are carried by global systems while the broad bands are carried by local systems. Considerations of the width of the profile suggest that each narrow band would probably originate in a global system on a unique isomer of a particular hydride