The functional properties of proteins depend upon their three-dimensional structure (native state). All the information needed to specify this structure is contained within its amino acid sequence. Under suitable conditions, most small proteins will spontaneously fold to their native states. To understand the biological function of proteins one would, therefore, like to be able to deduce or predict the three-dimensional structure from the amino acid sequence. This we cannot do. On the other hand, simple models have been developed to design sequences which are able to fold to a given conformation. Good folder sequences are characterized by a large gap, compared with the standard deviation of contact energies among the amino acids, between the energy of the sequence in the native conformation and the lowest energy (threshold E-c) of the conformations structurally dissimilar to the native one. Designed sequences which conserve (in any way) this energy gap share a common set of (conserved) contacts, contacts which form the folding nucleus of the protein. At the basis of the folding of designed sequences, lattice model representation of the folding of small, single domain, real proteins, we systematically observe the presence of local elementary structures, elementary structures which are formed at the very early stages of the compaction process, and which build the folding nucleus when they assemble together. All designed sequences which conserve the energy gap, display the same folding mechanism, although those displaying larger gaps fold faster than those whose native energy lies closer to E-c.