High-spin states in Dy-155 have been studied by gamma-gamma coincidence measurements via the Sn-124(S-36,5n)Dy-155 reaction at a beam energy of 155 MeV. Additional information has also been extracted from the reaction Gd-156(He-3,4n)Dy-155 at 39 MeV beam energy. Eight rotational bands have been populated and observed up to high spin (I less-than-or-equal-to 93/2). The band features have been analysed within the framework of the cranked-shell model. The i13/2 neutron alignments and the h11/2 proton alignments are discussed. B(M1)/B(E2) ratios have also been extracted for the strongly coupled bands to deduce further information on the detailed structure of these bands. The highest states (above spin 30) of two of the negative-parity bands gain energy rapidly with respect to a rigid rotor, which is consistent with properties expected for terminating bands.