  The pi N --> eta N and eta N --> eta N partial wave T-matrices for the eight
lowest partial waves have been obtained in a three coupled channel model with
unitarity manifestly imposed. The two physical channels are pi_N and eta_N, and
the third channel, pi_pi_N is an effective, but unphysical two body channel
which represents all remaining processes. The pi_N elastic phase shifts and the
weighted data base of the pi- p --> eta n total and differential cross sections
are chosen as the input for the fitting procedure. A model containing a single
resonance in each of the three partial waves that dominates the eta production
at lower energies is compared with previous analyses, based on similar
assumptions. A multiresonance coupled channel model is introduced which
significantly improves the agreement with all input data. Our results are
compared with a complementary multiresonance coupled channel analysis that is
constrained with elastic and continuum production channels. The inclusion of
the fourth P11 resonance in the 1440 - 2200 MeV region further improves the
agreement between the analysis and the data.
