This paper considers the analysis and synthesis of control systems subject to two types of disturbance signals : white signals and signals with bounded power. The resulting control problem involves minimizing a mixed H-2 and H(infinity) norm of the system. It is shown that the controller shares a separation property similar to those of pure H-2 or H(infinity) controllers. Necessary conditions and sufficient conditions are obtained for the existence of a solution to the mixed problem. Explicit state-space formulas are also given for the optimal controller.