Whole-profile-fitting least-squares techniques are applied to simulated and experimental X-ray diffraction patterns of monatomic face-centred cubic (f.c.c.)-derived non-crystallographic nanoclusters to extract structure and size information. Three main structure types have been considered (cuboctahedral, icosahedral and decahedral). Nanocluster structure models have been generated within an original mathematical approach so as to be independent of a specific material. For each structure type, a log-normal size distribution is assumed and a phenomenological function is introduced to model possible additional size-related strain effects. The Debye function method (modified to increase computational efficiency) has been used to obtain the diffracted intensities of the nanocluster. Tests revealed the effectiveness of the method to recognize the structure types correctly and to estimate with good accuracy structure concentrations and size distributions. Application to a thiol-passivated gold nanoparticle sample is presented.