We study the effect of 3D topological insulator (TI) contributions to the band structure and wavefunctions of quasi-one-dimensional electron systems (Q1DES). Our model for this system consists of an effective Hamiltonian derived previously in the literature from the crystal symmetries of Bi2Se3. We find that in wires whose face lies in the plane formed by the y and z crystal directions and whose width is around 25 quintuple layers or more, the bands nearest to the gap are non-monotonic; we show that this has implications for the conductance of the wire. In addition, we observed increasing penetration depth of surface states with increasing wavenumber of the propagating mode. We believe these results have qualitative relevance to the family of 3D topological insulators whose crystal structure is characterised by the space group Equation 1, and that the work done here contributes to the wider field of the study of conductance in topological insulators.