In time-invariant linear quadratic optimal control problems there is a hidden ‘ideal model’ automatically encoded into each performance indexJ. These hidden ideal models, which are themselves linear and lower order than the original plant, are not visible under cursory examination ofJand have apparently been overlooked by many professors, textbook writers and industrial users of linear quadratic control theory. In this paper, a special cost-decomposition procedure is described that will uncover these concealed ideal models and clearly show their relevance to the original optimization problem. Three examples are worked out.