The laser desorption of C-60 or C-70 fullerenes yields a distribution of ions with masses corresponding to an even number of carbon atoms around integer multiples of 60 or 70. Clusters with 120 or 140 atoms have been characterized as large coalesced fullerenes and fullerene dimers joined by a [2+2] cycloaddition. Several structures had been proposed for the species with less than an integer multiple of 60 or 70 atoms, but none of them has been validated experimentally. We have examined C-n (n = 112, 114, 116, 118, 136, and 138) cations and anions using high resolution ion mobility measurements and compared the results with trajectory calculations for a number of candidate geometries. We find that these species exist as near-spherical cages and [2+2] cycloadducts of smaller fullerenes derived from C60 Or C70 Quadruply bound C-116, C-118, C-136, and C-138 isomers that would result from the stepwise elimination of Ct from the preformed [2+2] C-60 or C-70 dimers were not observed. Hence the fullerene dimers lacking a few atoms are formed by coalescence of dissociation products rather than by dissociation of the products of coalescence. Plausible reasons why the [2+2] cycloadducts are the only dimers produced by the laser desorption of fullerenes are discussed.