The shells of ammonoid cephalopods are among the most recognizable fossils, whose fractally folded, internal walls (septa) have inspired many hypotheses on their adaptive value. The enduring explanation for their iterative evolution is that they strengthen the shell against pressure at increasing water depths. The fossil record does not definitively support this idea and much of the theoretical mechanical work behind it has suffered from inaccurate testing geometries and conflicting results. By using a different set of mathematical methods compared with previous studies, I generate a system of finite-element models that explore how different parameters affect the shell's response to water pressure. Increasing the number of initial folds of the septa ultimately has little to no effect on the resulting stress in the shell wall or the septum itself. The introduction of higher-order folds does reduce the tensile stress in the shell wall; however, this is coupled with a higher rate of increase of tensile stress in the septum itself. These results reveal that the increase in complexity should not be expected to have a significant effect on the shell's strength and suggests that the evolution of ammonitic septa does not reflect a persistent trend towards deeper-water habitats.