Nonmechanical beam steering technologies utilizing acoustooptics enable us to achieve the high-bandwidth laser beam positioning required for optical communications, laser scanners, ladars, etc. The properties of the Bragg cell, which are chiefly responsible for the efficiency and attainable characteristics of the entire positioning system, are ensured by the successful design of this optical component. However, the design of Bragg cells is dominated by the experience and intuition of the designers, and the potential of this technology is not fully utilized. An optimal Bragg cell design problem is formulated on the basis of known equations of the underlying physical phenomena, and a genetic optimization scheme is applied for the solution of the resulting formidable problem. The approach not only yields a design solution, but also enables one to vary the design criterion and emphasize particular properties of the resultant component. The prowess of the proposed approach is demonstrated by design optimization examples.