It is shown that the sequence-ordering tendencies induced by design into different fast-folding, thermally stable native structures interfere. This interference results in a type of quasiorthogonality between optimal native structures, which divides sequence space into fast-folding, thermally stable families surrounded by slow-folding, low stability shells. A concrete example of this effect is provided by using a simple alpha carbon type model in which a complete correspondence is established between sequence and structure. It is speculated that gaps can occur in the space of protein-like sequences separating the sequence families and resulting in a mechanism for stability and diversity of protein sequence information.