Near-wall resolution requirements make Large Eddy Simulation (LES) prohibitively expensive for high Reynolds number boundary layers. Typically, to alleviate the resolution requirement ad hoc models for the wall stresses are used to model the effects of the unresolved near-wall flow. However, even in turbulent channel flow, these models are often deficient. To determine if wall stress models can be improved we pose and solve a suboptimal control problem in turbulent channel flow. In this framework, the control is the unknown wall stresses and the objective is to achieve the correct low-order statistics in the interior of the flow. The solution of the control problem is used to construct a simple, much improved, wall stress model for turbulent channel flow.