Experimental data are presented for the scattering of electrons by CF2Cl2 and CF3Cl for both integral and backward scattering, from 2 eV (for CF2Cl2) and 0.65 eV (for CF3Cl) down to energies of 10 meV to 20 meV, with an energy resolution ranging from 0.75 meV to 1.5 meV (full width at half maximum) in the electron beam. Both molecules have dipole moments of similar to0.5 D and are expected to show very similar rotationally inelastic scattering cross sections. Cross sections for CF2Cl2 are, however, much larger at low energy than for CF3Cl, attributed to short-lived attachment of electrons to CF2Cl2. CF3Cl displays powerful suppression of rotational excitation in the forward direction, most strongly around 70 meV impact energy. This is ascribed to interference between a direct channel of rotational excitation and indirect excitation via a short-lived negative ion state.