  Rotational bands in $^{158}$Er at ultra-high spin have been studied in the
framework of relativistic and non-relativistic nuclear density functional
theories. Consistent results are obtained across the theoretical models used
but some puzzles remain when confronted with experiment. Namely, the many-body
configurations which provide good description of experimental transition
quadrupole moments and dynamic moments of inertia require substantial increase
of the spins of observed bands as compared with experimental estimates, which
are still subject to large uncertainties. If, however, the theoretical spins
assignments turned out to be correct, the experimental band 1 in $^{158}$Er
would be the highest-spin structure ever observed.

Nuclear Theory