We analyze the electronic properties of quantum wires with a Z-like profile within four-band models for the valence band of a semiconductor of diamond and zinc blende type. Group-theoretical considerations show that the valence-band structure is doubly degenerate only when the linear k-terms (coming e.g. from the bulk crystal inversion asymmetry) are neglected. The considerations apply to the more general case of a profile containing a 2D center of inversion.