An investigation is made of the extent to which low-energy $\pi N$ scattering is determined by the $N$ and $\Delta$ poles and the low-energy theorems. The on-shell amplitudes are expanded in ($\frac{{\mu }_{\pi }}{M_N}$) at fixed ($\frac{\nu }{{\mu }_{\pi }}$) and ($\frac{t}{{{\mu }_{\pi }}^2}$), and it is assumed that $M_{\Delta }-M_N=O\left({\mu }_{\pi }\right)$, in contrast to $M_{\mathrm{res}}-M_N=O\left(M_N\right)$ for all other resonances. The invariant amplitudes are determined using fixed-$t$ dispersion relations and are calculated to second order in ($\frac{{\mu }_{\pi }}{M_N}$). The crossing-odd amplitudes are fully determined by the $N$ and $\Delta$ poles and the low-energy theorems. The crossing-even amplitudes receive undetermined background contributions described by three expansion coefficients. If they are fixed using the "experimental" scattering lengths, the resulting model is in fairly good agreement with experiment.

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