A new data anal. methodol. for X-ray absorption near-edge spectroscopy (XANES) is introduced and tested using several examples. The methodol. has been implemented within the context of a new Matlab-based program discussed in a companion related article [Delgado-Jaime et al. (2010), J. Synchrotron Rad. 17, 132-137]. The approach makes use of a Monte Carlo search method to seek appropriate starting points for a fit model, allowing for the generation of a large no. of independent fits with minimal user-induced bias. The applicability of this methodol. is tested using various data sets on the Cl K-edge XAS data for tetragonal CuCl42-, a common ref. compd. used for calibration and covalency estn. in M-Cl bonds. A new background model function that effectively blends together background profiles with spectral features is an important component of the discussed methodol. The development of a robust evaluation function to fit multiple-edge data is discussed and the implications regarding std. approaches to data anal. are discussed and explored within these examples. [on SciFinder(R)]