  We consider a gas of $N$ bosons in a box with volume one interacting through
a two-body potential with scattering length of order $N^{-1}$ (Gross-Pitaevskii
limit). Assuming the (unscaled) potential to be sufficiently small, we show
that the ground state of the system and all states with relatively small
excitation energy exhibit complete Bose-Einstein condensation, with a uniform
(i.e. $N$ independent) bound on the number of excitations.
