  We study the change in condensation energy from a single pair of fermionic
atoms to a large number of pairs interacting via the reduced BCS potential. We
find that the energy-saving due to correlations decreases when the pair number
increases because the number of empty states available for pairing gets smaller
("moth-eaten effect"). However, this decrease dominates the 3D kinetic energy
increase of the same amount of noninteracting atoms only when the pair number
is a sizeable fraction of the number of states available for pairing. As a
result, in BEC-BCS crossover of 3D systems, the condensation energy per pair
first increases and then decreases with pair number while in 2D, it always is
controlled by the "moth-eaten effect" and thus simply decreases.
