This paper examines the problem of guiding a missile to a target using minimal energy. First, an optimal controller is developed for a missile that has arbitrary control over its acceleration vector. Next, an optimal controller is sought for a missile that has a directional control constraint, which is intended to model the actual constraint present in aerodynamically controlled missiles. The optimal guidance law is shown to have a very convenient form that is directly related to the optimal guidance law without the control constraint. Simulation results are conducted to completely characterize the new guidance law.