The dissociation energies of CN and C-2 are determined with multireference configuration-interaction calculations utilizing very large Gaussian basis sets. Valence level one-particle errors, such as basis set incompleteness and basis set superposition error, are essentially eliminated by extrapolation. The errors in the correlation, or n particle, treatment are considered in detail. The effect of 1s correlation is computed using the averaged coupled-pair functional approach. Our best estimate for C-2 is in very good agreement with the recent experimental result by Urdahl et al. Our best D-0 value for CN is 7.72+/-0.04 eV. This is larger than previous theoretical values and in good agreement with the recent experimental result (7.738+/-0.02 eV) of Huang et al. The origin of the differences between the current D-0 and our previous theoretical value is discussed.