We design two components of an American football helmet (composite shell and foam liner) to illustrate the efficacy of a goal-oriented, inverse decision-based design method for multi-component product design. The method is goal-oriented because we first identify the end performance system level goals for the helmet, namely, dissipate impact energy, minimize impulse, and minimize helmet weight. We arrange the components in the order that they receive impact energy and then find satisficing solutions for the foam liner to achieve the system-level goals as close as possible, and then we adjust the targets for the composite shell to reduce the helmet weight without a substantial loss in performance. We use the Concept Exploration Framework to systematically gather information about each component, and the compromise Decision Support Problem to generate satisficing solutions under uncertainty. Finally, we verify our design decisions with Finite Element Analysis. Although the results are interesting, our focus is to establish the efficacy of the inverse method for the design of an American football helmet.