  In a previous paper we demonstrated that Bethe's equations are not sufficient
to specify the eigenvectors of the XXZ model at roots of unity for states where
the Hamiltonian has degenerate eigenvalues. We here find the equations which
will complete the specification of the eigenvectors in these degenerate cases
and present evidence that the $sl_2$ loop algebra symmetry is sufficiently
powerful to determine that the highest weight of each irreducible
representation is given by Bethe's ansatz.
