The main purpose of this article is to show that photogrammetric bundle-adjustment computations can be sequentially organized into modules. Furthermore, the chain rule can be used to simplify the computation of the analytical Jacobians needed for the adjustment. Novel projection models can be flexibly evaluated by inserting, modifying, or swapping the order of selected modules. As a proof of concept, two variants of the pinhole projection model with Brown lens distortion were implemented in the open-source Damped Bundle Adjustment Toolbox and applied to simulated and calibration data for a nonconventional lens system. The results show a significant difference for the simulated, error-free, data but not for the real calibration data. The current flexible implementation incurs a performance loss. However, in cases where flexibility is more important, the modular formulation should be a useful tool to investigate novel sensors, data-processing techniques, and refractive models.