To divide, Gram-negative bacterial cells must remodel their peptidoglycan cell wall to a smaller and smaller radius at the division site, but how this process occurs remains debated. While the tubulin homolog FtsZ is thought to generate a constrictive force, it has also been proposed that cell wall remodeling alone is sufficient to drive membrane constriction, possibly via a make-before-break mechanism in which new hoops of cell wall are made inside the existing hoops (make) before bonds in the existing wall are cleaved (break). Previously, we constructed software, REMODELER 1, to simulate cell wall remodeling in rod-shaped bacteria during growth. Here, we used this software as the basis for an expanded simulation system, REMODELER 2, which we used to explore different mechanistic models of cell wall division. We found that simply organizing the cell wall synthesis complexes at the midcell was not sufficient to cause wall invagination, even with the implementation of a make-before-break mechanism. Applying a constrictive force at the midcell could drive division if the force was sufficiently large to initially constrict the midcell into a compressed state before new hoops of relaxed cell wall were incorporated between existing hoops. Adding a make-before-break mechanism could drive division with a smaller constrictive force sufficient to bring the midcell peptidoglycan into a relaxed, but not necessarily compressed, state.