Poles and resonances are used to find χ2 fits to the data up to several hundred MeV above threshold for the processes π-+p-->n+η and γ+p-->p+η. Below center-of-mass energy W=1700 MeV, a consistent picture of these reactions is achieved with the following ingredients: a nucleon pole and P11(1400), S11(1570), and D13(1512) resonances for production by pions; a nucleon pole, a vector meson pole, and S11(1570) and D13(1512) resonances for photoproduction. Some F15(1688) also improves the fits. The value of the η-nucleon coupling constant, gη24π is <~0.002 in both processes. Implications of these results for quark models and SU(3) symmetry are discussed. Above W=1700, possible additional resonances are considered in η production by pions.