We present a detailed study of the mechanism by which the INVERT method (Cliffe et al 2010 Phys. Rev. Lett. 104 125501) guides structure refinement of disordered materials. We present a number of different possible implementations of the central algorithm and explore the question of algorithm weighting. Our analysis includes quantification of the relative contributions of variance and fit-to-data terms during structure refinement, which leads us to study the roles of density fluctuations and configurational jamming in the RMC fitting process. We present a parametric study of the pair distribution function solution space for C60, a-Si and a-SiO2, which serves to highlight the difficulties faced in developing a transferable weighting scheme.