The organization of chains of oligopeptidoglycan in the saccular wall is of critical importance in the study of the mechanism and physiology of prokaryotic wall growth. The electron microphotographs of De Pedro et al. present new findings and can be used to negate or at least raise questions about the previously accepted conclusion that the glycan chains are oriented transversely to the axis of rod-shaped Escherichia coli. This suggests caution in assuming that the glycan chains in the murein structure are parallel to each other and are perpendicular to the axis of the cell. These results should reopen the question of not only the orientation of the peptidoglycan chains, but the possibility of variability in orientation. Three classes of hypotheses about wall growth are reconsidered and problems with them are presented. The new results from De Pedro's laboratory and the experimental glycan chain length distribution argue against proposed systematic models. These include models that postulate belts or hoops stretched around the circumference of the cell and mechanisms that insert new chains of the length of presumptive "docking" strands in the stress-bearing wall. They are consistent, however, with the surface stress theory that proposes that random enzyme action together with physical forces are involved in the elongation of the rod-shaped Gram-negative wall.