We use an empirical tight-binding approach to calculate electron and hole states in [111]-grown PbSe nanowires. We show that the valley-orbit and spin-orbit splittings are very sensitive to the atomic arrangement within the nanowire elementary cell and differ for [111]-nanowires with microscopic $D_{3d}$, $C_{2h}$ and $D_{3}$ symmetries. For the nanowire diameter below 4 nm the valley-orbit splittings become comparable with the confinement energies and the $boldsymbol{k}cdotboldsymbol{p}$ method is inapplicable. Nanowires with the $D_{3}$ point symmetry having no inversion center exhibit giant spin splitting $E = alpha k_z$, linear in one-dimensional wave vector $k_z$, with the constant $alpha$ up to 1 eV$cdot$AA.
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