  We study the reaction $\pi^\pm p \to \pi^\pm \pi^+ n$ and $\pi^- p \to \pi^0
\pi^0 n$ in heavy-baryon chiral perturbation theory of chiral order three from
threshold up to pion laboratory kinetic energies of 400 MeV. We find that the
contributions from amplitudes of chiral order three are large and play an
essential role in reproducing the experimental data.
