Abstract Systematic calculations of non-collective single-neutron states in a series of transitional Th isotopes with A=219−229 have been performed using the reflection-asymmetric mean field theory with an average Woods-Saxon potential and a monopole pairing residual interaction. Calculated band-heads and equilibrium deformations of the lowest single-neutron states are presented. Strong polarization effects due to the odd neutron explain the systematic trends of known band-heads. A pronounced odd-even staggering seen in the calculated octupole barriers has been found and explained in terms of the specialization energy. The influence of higher-multipolarity deformations is discussed.