Recently Irle. Morokuma, and collaborators have carried Out a series of quantum chemical molecular dynamics simulations of carbon clustering. The results of these computer experiments are that carbon clusters of size greater than 60 atoms are rapidly formed, anneal to giant fullerenes, and then these fullerenes shrink. The simulation could not be carried to long enough times for the shrinking to reach C-60, but they propose reasonably that this shrinking process ultimately forms buckminsterfullerene. However, these simulations do not reveal the force driving the shrinking process. Here, this driving force for shrinking is found to be reactions in which Q is swapped between fullerenes. The key element is that for typical fullerenes the equilibrium constants for such C, interchanges are near unity, resulting in expansion of the breadth of the fullerene distribution in an annealing process. When fullerenes of 60 or 70 atoms are populated by shrinking, they fall into the local energy minimum of buckminsterfullerene or D-5h C-70. This simple mechanism accounts for the high yields (>20%) of buckminsterfullerene that can be achieved in pure carbon systems.