Fluorescence recovery after photobleaching (FRAP) measurements offer an important tool for analyzing diffusion and binding processes. Confocal scanning laser microscopes that are used in FRAP experiments bleach regions with a radially Gaussian distributed profile. Previous attempts to derive analytical expressions in the case of processes governed by fast diffusion have overlooked the characteristics of the instruments used to perform FRAP measurements and therefore led to approximating solutions. In the present paper, bleaching laser beam characteristics are incorporated into an improved model to provide a more rigorous and accurate method. The proposed model simulates binding inside bounded regions, and it leads to FRAP curves that depend on the on and off rates that can be employed to determine the rate constants. It can be used in conjunction with experimental data acquired with confocal scanning laser microscopes to investigate the biophysical properties of proteins in living cells. The model aims to improve the accuracy when determining rate constants by taking into account a more realistic scenario of the light-matter interaction.