We propose a method to analyze x-ray-absorption fine-structure data that avoids an arbitrary restriction of the size of the model-parameter space. It starts with an a priori guess of the model parameters which is introduced into the fitting procedure by Bayesian arguments. Two different descriptions are discussed to determine the relative impact of the a priori and experimental information on the fit. The resulting algorithms are tested by application to three simulated experiments at the Ta L3-edge and to Cu K-edge data.