Abstract 4D-Var (four-dimensional variational data assimilation) has enjoyed notable success as a component of numerical weather prediction over the past several decades. Its success stems in part from its aesthetic appeal as well as its pragmatism. Yet, optimization of the traditional cost functions used in weather prediction via 4D-Var deserves further attention — especially in those situations where adequacy of data is a major concern. We explore the results of 4D-Var output in these situations where the fine structure of solutions come from an equivalent yet much more computationally costly method, the forward sensitivity method (FSM). FSM makes use of the time evolution of model-output sensitivity as the means of finding the optimal solution to the data assimilation problem. After development of the underlying theory that permits comparison of the two methods, we apply the theory to a simplified yet physically meaningful and easy to interpret air/sea interaction model. Results indicate that strategic placement of observations is critical to the success of 4D-Var, where placement is fundamentally tied to the sensitivity of model output to the elements of control.