Study of the energy levels of /sup 156/Dy through the /sup 159/Tb(/b p/,4/b n/)/sup 156/Dy reaction has revealed the existence of six states with excitation energies between 1.8 and 2.8 MeV and spins between 6 and 12. Some of them can tentatively be assigned as low-spin members of `upper' bands which are thought to be responsible for the backbending phenomenon experimentally observed in the ground-state of beta -vibrational bands of this nucleus. Others could be levels of a negative-parity octupole band.Anglai