The structure of benzene:ethane co-crystal at 90 K is refined with anisotropic displacement parameters without geometric restraints from high-resolution synchrotron X-ray powder diffraction (XRPD) data using the derivative difference method (DDM) with properly chosen weighting schemes. The average C-C bond precision achieved is 0.005 Å and the H-atom positions in ethane are refined independently. A new DDM weighting scheme is introduced that compensates for big distortions of experimental data. The results are compared with density functional theory (DFT) calculations reported by Maynard-Casely et al. [(2016). IUCrJ, 3, 192-199] where a rigid-body Rietveld refinement was also applied to the same dataset due to severe distortions of the powder pattern attributable to experimental peculiarities. For the crystal structure of 2-aminopyridinium fumarate-fumaric acid formerly refined applying 77 geometric restraints by Dong et al. [(2013). Acta Cryst. C69, 896-900], an unrestrained DDM refinement using the same XRPD pattern surprisingly gave two times narrower dispersion of interatomic distances.