This paper proposes a new design method of robust servo systems for step references and step disturbances. In this method, the tracking characteristics for step references and the feedback characteristics for step disturbances can be determined optimally, using independent quadratic-integral performance indices. Thus, it provides a two-degree-of-freedom design method of control systems in the context of linear-quadratic optimal control. The design procedure consists of two steps. In the first step, a servo system without integral compensation achieving the optimal responses to step references is designed. In the second step, an integral compensator is incorporated, and the feedback gain is determined so as to achieve the optimal responses to step disturbances, without changing the responses to step references. It is shown that as the ’state weighting matrix’ becomes larger in the second step, the responses to step disturbances become quicker, and that they monotonically tend to the responses of an ’ideally disturbance-rejected system’ (i.e. the system with the ideal disturbance compensation input).