A classic region of band termination at high spin occurs in rare-earth nuclei with around ten valence nucleons above the ¹⁴⁶Gd closed core. Results are presented here for such non-collective oblate (γ = 60°) terminating states in odd-Z ¹⁵⁵Ho, odd-odd ¹⁵⁶Ho, and even-even ¹⁵⁶Er, where they are compared with neighbouring nuclei. In addition to these particularly favoured states, the occurrence of collective triaxial strongly deformed (TSD) bands, bypassing the terminating states and extending to over 65h, is reviewed.