Combined optimal embodiment design and control is increasingly necessary in designing modern artifacts. Several strategies for achieving such a system-level optimum were examined previously in the context of a case study. Since different strategies often lead to different results, a more comprehensive understanding of the relative advantages and disadvantages of these “concurrent design” processes is desirable. The present article explores this question using a very simple problem to demonstrate the complexities involved. Monotonicity analysis and a decomposition framework help explain the reasons for arriving at different results, even unexpectedly. Conclusions are drawn regarding the effectiveness of the various modeling formulations.