We present a hierarchical framework for approximately-optimal control of redundant manipulators. The plant is augmented with a low-level feedback controller, designed to yield input-output behavior that captures the task-relevant aspects of plant dynamics but has reduced dimensionality. This makes it possible to reformulate the optimal control problem in terms of the augmented dynamics, and optimize a high-level feedback controller without running into the curse of dimensionality. The resulting control hierarchy compares favorably to existing methods in robotics. Furthermore we demonstrate a number of similarities to (non-hierarchical) optimal feedback control. Besides its engineering applications, the new framework addresses a key unresolved problem in the neural control of movement. It has long been hypothesized that coordination involves selective control of task parameters via muscle synergies, but the link between these parameters and the synergies capable of controlling them has remained elusive. Our framework provides this missing link.