The energy spectrum of C-60 nonclassic fullerenes with single heptagon defects calculated by Brenner empirical potential is found to submerge into the spectrum of classic fullerenes. Geometry analysis indicates that these nonclassic fullerene isomers can be more attainable than classic fullerenes at higher Stone-Wales (SW) stacks. Molecular dynamic simulations of the C-60 isomer evolution in He buffer gas at 2500 K demonstrate that nonclassic fullerenes, especially those with heptagon defects, play an important role in the dynamics of C-60 annealing, and that the Stone-Wales stack-by-stack transition mainly occurs at lower SW stacks. A non-SW multistep rearrangement is first observed in the simulation with its transition sequence and intermediate state presented in detail. (C) 2004 American Institute of Physics.