The performance of a closed loop adaptive optics system may in principle be improved by selecting distinct and independently optimized control bandwidths for separate components, or modes, of the wave front distortion profile. In this paper we outline a method for synthesizing and optimizing a multi-bandwidth adaptive optics control system from performance estimates previously derived for single-bandwidth control systems operating over a range of bandwidths. Numerical results are presented for use of an atmospheric turbulence profile consisting of a single translating phase screen with Kolmogorov statistics, a Shack-Hartmann wave front sensor with 8 subapertures across the aperture of the telescope, and a continuous facesheet deformable mirror with actuators conjugate with the corners of the wave front sensor subapertures. The use of multiple control bandwidths significantly relaxes the wave front sensor noise level allowed for the adaptive optics system to operate near the performance limit imposed by fitting error. Nearly all of this reduction is already achieved through the use of a control system utilizing only two distinct bandwidths, one of which is the zero bandwidth.