The large electron affinity of fullerenes such as C-60 or C-70 has been rationalized by taking into account the effects of molecular size, the number of five-membered rings, and pyramidalization on their LUMO energy. The study of conjugated cyclopolyenes having different size and pyramidalization has shown an enhancement of their electron affinity upon an increase in these two factors and with the presence of pentagonal instead of hexagonal rings. It has also been found that pyramidalization has an effect which is almost constant for all the systems studied, namely, a reduction of the LUMO energy by a similar extent. The stabilization of the LUMO orbital due to an increase in the molecular size is normally more determining than the effect of pyramidalization. The results obtained indicate that fullerenes exhibit enhanced electron-withdrawing character upon increase of their molecular size and pyramidalization.