Both force-field (MMPI) and AM1 (restricted and unrestricted HF) calculations are herein used to investigate the underlying reasons for the fullerene-fulleroid structural dichotomies observed in carbene, silylene, nitrene, and oxygen adducts of C-60. Via the investigation of a series of model systems, it is demonstrated that curvature actually favors the open, fulleroid structure; this effect of curvature on the norcaradiene-cycloheptatriene equilibrium is general. Strategies for the creation of 6,6-bridged fulleroids are suggested.