  We evaluate the cross sections for the dissociation of $J/\psi$ and $\psi'$
by $\pi$ and $\rho$ at low collision energies, using the quark-interchange
model of Barnes and Swanson. The dissociation cross section for $J/\psi$ by
$\pi$ is found to be relatively small with a maximum of about 1 mb and a
kinetic energy threshold of 0.65 GeV. The pion-induced $\psi'$ dissociation
cross section is found to be much larger, with a maximum of about 5 mb and a
lower threshold. Dissociation cross sections for $J/\psi$ and $\psi'$ by $\rho$
mesons are also evaluated and are found to be large near threshold.
