Models are built of crystalline random copolymers in which the degree of longitudinal register between adjacent chains is varied by moving the chains relative to each other within a prescribed axial range. The chains are placed at the relative positions which give the greatest total number of ethylene glycol matches between them. The models are built without any disposition to create matches between identical contiguous sequences of units, or any other type of imposed register. Calculation of diffraction patterns from both two- and three-dimensional models, shows that a good fit to the experimental data occurs with a level of register which is achieved after comparatively little longitudinal shuffling (searching). While this best-fit model shows some evidence of sequence matched entities, they are shorter and less regular than those envisaged in previous studies.