Identification of the carriers of the enigmatic Diffuse Interstellar Bands (DIBs) is the biggest challenge in astronomical spectroscopy. The observational data comprise a catalogue of over 400 interstellar absorption features, predominantly at visible wavelengths, and are observed towards bright O and B stars seen though significant foreground material. Despite this field of work being first established nearly a century ago, the determination of a carrier of any of these bands has so far proved unsuccessful. It is anticipated that solving this problem would open up a new probe of interstellar conditions and processes, possibly with far-reaching implications for our understanding of interstellar chemistry. In this talk, I will present an analysis of the profile of the 6614 Å DIB; a band that is unusual in having fine structure. The substructure seen varies between sightlines, and the differences are attributable to the level of internal excitation of the carrier. I will demonstrate how the band profile can be disentangled into a main origin band and weaker hot-bands, and will present rotational modelling results, which suggest that the carrier is a large carbon-based molecule with about 20 heavy atoms.