The issue of whether short chain branches in polyethylene are tolerated within the crystalline component, or rejected from it, is longstanding and controversial. We have re-examined this issue by combining new X-ray diffraction techniques with molecular modelling. The X-ray diffraction patterns were recorded from a series of polyethylenes covering a broad range of branch types, contents and distributions, in both unoriented and fibre sample forms. This paper is the third and final in a sequence investigating the structure of this series. After unit cell parameters had been determined by whole pattern fitting, relative intensity ratios were measured to detect any systematic changes as functions of branch type, content and distribution. Previous studies have investigated only changes in the unit cell parameters. The influence of paracrystalline distortions was taken into account. Significant changes were found in three intensity ratios, which decreased as a function of branch concentration and increased as a function of the degree of heterogeneity (blockiness) in branch distribution. Molecular modelling showed that only branch inclusion was compatible with the experimental intensity changes. The modelling indicated that the branches were incorporated into the crystalline lattice via distortion of the neighbouring chains, mainly in the direction parallel to the unit cell a axis direction. The length of the branch backbone fitted into the lattice by lying approximately parallel to the unit cell c-axis (the main chain direction), emulating a section of a main chain. Another finding from the modelling concerned the extent of inclusion in the more highly branched samples (typically 15-20 SCB/1000C, linear low density polyethylene). For models of these samples, branches could only be tolerated within a unit cell having the experimental values of unit cell parameters at concentrations around 3 SCB/1000C, substantially lower than in the bulk material. At higher incorporated branch concentrations, crystalline packing of the chains was not maintained during model minimisation. For such polyethylenes, branches must therefore be partitioned between the crystalline and amorphous regions. These modelling findings provide a theoretical basis for the recent, similar experimental findings from solid-state C-13 nuclear magnetic resonance spectroscopy.