We introduce the family of limited model information designs, which construct controllers by accessing the plant's model in a constrained manner. We investigate the closed loop performance of the best controller that they can produce. For a class of linear discrete-time, time invariant plants, we show that there exists a limited model information control design which results in a controller whose performance is in a bounded neighborhood of the optimal control design and we show that this controller is the best controller that one can design with limited information about the plant model. We investigate the plant model structure and the model information on this neighborhood.