While theoretical standards such as those from FEFF have many advantages for EXAFS analysis, the quality of fit statistics and estimation of parameter uncertainties has always been somewhat problematic using them. Even though the calculations reproduce EXAFS features sufficiently well to give bond distances accurate to 0.01Å or so, fits to high-quality experimental spectra will have fit residuals far larger than the experimental uncertainties. One of the possible causes for this mis-fit is from approximations made in the phenomenological calculations of the inelastic losses, though this has been difficult to test conclusively in the past. Recent improvements in calculations of inelastic losses using a many-pole self-energy (MPSE) using a real-space calculation of the dielectric function have been shown to give significant improvements in XANES calculations. Here, we discuss the use of MPSE calculations for EXAFS analysis, and show that these calculations from FEFF8.5 can quantitatively improve fit quality for EXAFS, reducing mis-fits by a factor of 2 or more compared to FEFF6. This approach may also allow the semi-physical fit parameter S₀² to be avoided. The implications for improving precision for EXAFS analysis and the nature of the remaining fit residual are discussed.