Context. Recent calculations have shown that the UV bump at about 217.5 nm in the extinction curve can be explained by a complex mixture of polycyclic aromatic hydrocarbons (PAHs) in several ionisation states. Other studies proposed that the carriers are a restricted population made of neutral and singly-ionised dehydrogenated coronene molecules (C 24 H n , n ≤ 3), in line with models of the hydrogenation state of interstellar PAHs predicting that medium-sized species are highly dehydrogenated. Aims. To assess the observational consequences of the latter hypothesis we have undertaken a systematic theoretical study of the electronic spectra of dehydrogenated PAHs. We use our first results to see whether such spectra show strong general trends upon dehydrogenation. Methods. We performed calculations using state-of-the-art techniques in the framework of the density functional theory (DFT) to obtain the electronic ground-state geometries, and of the time-dependent DFT to evaluate the electronic excited-state properties. Results. We computed the absorption cross-section of the species C 24 H n (n = 12, 10, 8, 6, 4, 2, 0) in their neutral and cationic charge-states. Similar calculations were performed for other PAHs and their fully dehydrogenated counterparts. Conclusions. π-electron energies are always found to be strongly affected by dehydrogenation. In all cases we examined, progressive dehydrogenation translates into a correspondingly progressive blue shift of the main electronic transitions. In particular, the π → π * collective resonance becomes broader and bluer with dehydrogenation. Its calculated energy position is therefore predicted to fall in the gap between the UV bump and the far-UV rise of the extinction curve. Since this effect appears to be systematic, it poses a tight observational limit on the column density of strongly dehydrogenated medium-sized PAHs.