This paper addresses the problem of obtaining nonlinear state-feedback controllers for controlling constrained dynamic systems, a problem which is, perhaps, the most important outstanding problem in control design. A novel off-line, optimization-based design procedure is employed; the control law is constructed from the solution to a finite number of optimal open-loop control problems. The design procedure permits relatively simple modification and improvement to the control law to be made in those regions of the state-space in which simulation reveals deficiencies. This potential for incremental improvement constitutes an important advantage over alternative methods. The results are relevant when high performance is required of systems subject lo constraints on controls and states.