The bandstructures of [110] and [001] Bi<inf>2</inf>Te<inf>3</inf> nanowires are solved with the atomistic 20 band tight binding functionality of NEMO5. The theoretical results reveal: The popular assumption that all topological insulator (TI) wire surfaces are equivalent is inappropriate. The Fermi velocity of chemically distinct wire surfaces differs significantly which creates an effective in-surface confinement potential. As a result, topological insulator surface states prefer specific surfaces. Therefore, experiments have to be designed carefully not to probe surfaces unfavorable to the surface states (low density of states) and thereby be insensitive to the TI-effects.