The coincidence of multiple x-rays in a detection cell within one CCD frame - an effect known as pile-up - is a significant source of spectral contamination for bright sources observed with the AXAF CCD Imaging Spectrometer (ACIS). Investigation of algorithms for correcting contaminated spectra is underway. In cases where such algorithms fail, the observer may wish to discard events from the core of the AXAF point spread function (PSF), computing spectra using only events from the PSF wings, where pile-up effects are reduced. This work investigates the effectiveness of this technique for an isolated on-axis point source, using event lists produced by a Monte-Carlo simulation of the ACIS instrument.