The authors have reported elsewhere (Chem. Eng. Sci., 146, 337, 2016) a new method that derives models of micro-packed beds (μPBs) of near-spherical particles from X-ray microtomography grayscale images of limited resolution compared to the characteristics dimensions of the particles and porosity. The new method is distinguished by it not requiring a grayscale threshold to partition the images into solid and void phases, and its retention of the underlying spherical geometry, two issues that are particularly problematic when more traditional approaches are used to build models of μPBs. Here it is shown that a Reverse Monte Carlo (RMC) algorithm combined with Simulated Annealing (SA) can refine the models obtained from this new method to eliminate the vast majority of particle overlaps and incorporate particle size distributions. Application of the RMC-SA to an initial model of a μPB yielded a porosity estimate that was, within experimental uncertainty, the same as its directly measured counterpart. It was further shown that the porosity of μPBs is near unity at the bed wall and oscillates in a decaying fashion normal to the wall up to a distance of around three particle diameters into the bed. This leads to the porosity decreasing with increasing bed-to-particle diameter ratio. The opposite was observed, however, for the average number of particle-particle contacts (the mean coordination number). This latter behaviour has two origins: one in which the bulk of the bed where the coordination number is maximal and constant exerts increasing influence (volumetric origin), and one in which the packing density inherently decreases with the bed-to-particle diameter ratio (packing origin).