Empirical data indicate that several good solvents for C-60 and [6,6]-phenyl-C61-butyric acid methyl ester (PCBM) have substantial polar and hydrogen-bonding components, which are not intrinsic to the structure of the C-60 and PCBM molecules themselves. Functional solubility parameter (FSP) and convex solubility parameter (CSP) computations are performed on C-60 and PCBM using solubility data available in the literature. The CSP and FSP results are compared to previously reported Hansen solubility parameters (HSPs) and to the parameters calculated using additive functional group contribution methods. The CSP and FSP methods confirm the anomalously large polar and hydrogen-bonding parameters, delta(P) and delta(H), obtained experimentally for C-60 and PCBM. This behavior, which is quite irregular given the structure of the molecules, is due to the fact that several good solvents have high delta(P) and delta(H) values. Thus, these irregularities are highlighted by the CSP and FSP calculations. Additional contradictory solubility characteristics are disclosed by comparing the experimental solubility parameters to a linear solvation energy relationship (LSER) model, additive functional group calculations, and COSMO-RS computations. The FSP solubility function strongly suggests that the solubility parameters do not accurately represent the cohesive energy density properties of C-60 and PCBM, as intended, but rather they manifest the properties of the solvents, e.g., high delta(P) and delta(H) values, that are necessary to accommodate these molecules in the liquid phase.