The photon density profile of an X-ray free-electron laser (XFEL) beam at the focal position is a critical parameter for serial femtosecond crystallography (SFX), but is difficult to measure because of the destructive power of the beam. A novel high intensity radiation induced phasing method (HIRIP) has been proposed as a general experimental approach for protein structure determination, but has proved to be sensitive to variations of the X-ray intensity, with uniform incident fluence desired for best performance. Here we show that experimental SFX data collected at the nano-focus chamber of the Coherent X-ray Imaging end-station at the Linac Coherent Light Source using crystals with a limited size distribution suggests an average profile of the X-ray beam that has a large variation of intensity. We propose a new method to improve the quality of high fluence data for HI-RIP, by identifying and removing diffraction patterns from crystals exposed to the low intensity region of the beam. The method requires crystals of average size comparable to the width of the focal spot.