Laser vaporization of a substrate within the throat of a pulsed nozzle is used to generate a supersonic beam of carbon clusters. The neutral cluster beam is probed downstream by UV laser photoionization with time-of-flight mass analysis of the resulting photoions. Using graphite as the substrate, carbon clusters Cn for n=1-190 have been produced having a distinctly bimodal cluster size distribution: (i) Both even and odd clusters for Cn, 1≤n≤30; and (ii) only even clusters C2n, 20≤n≤90. The nature of the bimodal distribution, and the intensity alterations in the observed C+n signals are interpreted on the basis of cluster formation and stability arguments. Ionizing laser power dependences taken at several different photon energies are used to roughly bracket the carbon cluster ionization potentials, and, at high laser intensity, to observe the onset of multiphoton fragmentation. By treating the graphite rod with KOH, a greatly altered carbon cluster distribution with mixed carbon/potassium clusters of formula K2C2n is produced.