The spin-restricted and spin-polarized fully self-consistent linear muffin tin orbital band calculations for cuprate CuGeO₃ are presented with Cu atoms in normal and displaced positions within the orthorhombic cells. This, computationally much cheaper, approach gives practically the same one-electron bands as recent linear augmented plane wave calculations, and the same qualitative explanation for the spin-Peierls transition observed at low temperatures in this compound. New self-consistent spin-polarized calculations of CuGeO₃, for some supposed antiferromagnetic order in copper chains along the orthorhombic c axis, have given very small values for magnetic moments on Cu atoms. Again the dimerization of CuO₂ chains can open a band gap at E_F, if the Cu displacements in neighbouring chains are out of phase.