The characterization of multilayer structures having individual layer thicknesses in the nanometer range is a non-trivial task due to the large num ber of parameters involved. To address this problem, hard X-ray grazing-incidence specular reflectivity measurements and data modeling were performed. However, strong correlations between parameters (e.g. thickness and density, roughness and density) were observed due to insufficient amount of information present in the experimental data. To circumvent this difficulty measurements were performed at various energies selected from the wide spectrum of a synchrotron X-ray source. The fitting procedure used a Markovian probabilistic optimization algorithm, known as simulated annealing, and a solution was searched for the ensemble of experimental data collected. Results obtained from measurements performed at X-ray energies of 12 keV, 15 keV, and 16 keV on an Ir/Al2O3 multilayer demonstrate the capabilities and present limitations of the method.