  In the framework of chiral model(s) based on the linear realization of chiral
symmetry, we investigate the low-energy phenomenological properties of the
nucleon and its chiral partner (identified with either $N(1535)$ or $N(1650)$)
in the naive assignment and compare the results with the ones obtained in the
mirror assignment. We find that, within the naive assignment, we are not able
to reproduce the experimental value of the isospin-odd scattering length, while
the mirror assignment is in good agreement with it for both choices $N(1535)$
and $N(1650)$. The isospin-even scattering length is not yet conclusive in
either assignment because it depends crucially on the poorly known scalar
mesonic sector. The decay with $\Gamma_{N(1535)\rightarrow N\eta }$ turns out
to be far too small in both the naive and mirror assignments, while
$\Gamma_{N(1650)\rightarrow N\eta}$ is described correctly by both of them. In
conclusions, the mirror assignment with $N(1650)$ as the chiral partner of the
nucleon is the favored configuration.
