We have measured electron impact ionization from the ground state of Fe^9+^ and Fe^10+^ over the relative electron-ion collision energy ranges 200-1900eV and 250-1800eV, respectively. The ions were confined in an ion storage ring long enough for essentially all metastable levels to radiatively relax to the ground state. For single ionization, we find a number of discrepancies between the existing theoretical cross sections and our results. The calculations appear to neglect some excitation-autoionization (EA) channels, particularly from n=3 to n' excitations, which are important near threshold, and those from n=2-->3 excitations, which contribute at about 650eV. Conversely, at higher energies the calculations appear to overestimate the importance of EA channels due to excitation into levels where n>=4. The resulting experimental rate coefficients agree with the most recent theory for Fe^9+^ to within 16% and for Fe^10+^ to within 19% at temperatures where these ions are predicted to form in collisional ionization equilibrium. We have also measured double ionization of Fe^9+^ forming Fe^11+^ in the energy range 450-3000eV and found that although there is an appreciable cross section for direct double ionization, the dominant mechanism appears to be through direct ionization of an inner shell electron producing an excited state that subsequently stabilizes through autoionization.