We report measurements of electron impact ionization (EII) for Fe^13+, Fe^16+, and Fe^17+ over collision energies from below threshold to above 3000 eV. The ions were recirculated using an ion storage ring. Data were collected after a sufficiently long time that essentially all the ions had relaxed radiatively to their ground state before data were collected. For single ionization of $\fethirteen$ we find that previous single pass experiments are more than 40% larger than our results. Compared to our work, the theoretical cross section recommended by Arnaud & Raymond (1992) is more than 30% larger, while that of Dere (2007) is about 20% greater. Much of the discrepancy with Dere (2007) is due to the theory overestimating the contribution of excitation-autoionization via n=2 excitations. Double ionization of Fe^13+ is dominated by direct ionization of an inner shell electron accompanied by autoionization of a second electron. Our results for single ionization of Fe^16+ and Fe^17+ agree with theoretical calculations to within the experimental uncertainties. ; Comment: Accepted for the Astrophysical Journal