We present x-ray absorption and emission experiments and ab initio calculations showing that the size of carbon diamond must be reduced to at least 2 nm, in order to observe an increase of its optical gap, at variance with Si and Ge where quantum confinement effects persist up to 6-7 nm. In addition, our calculations show that the surface of nanodiamond particles larger than approximately 1 nm reconstructs in a fullerenelike manner, giving rise to a new family of carbon clusters: bucky diamonds. Signatures of these surface reconstructions are compatible with pre-edge features observed in measured absorption spectra.