We propose and solve an optimal robust performance problem (ORPP), attempting minimal cost of feedback (i.e. sensor noise and control effort) in achieving the prescribed performance tolerance, and thereby minimizing the conservatism involved in a robust performance design. To solve the ORPP, a conservative solution to the robust performance problem (RPP) is obtained as an initial design using the mu-synthesis, then the Q-parameterization is applied to arrive at a suboptimal solution to the ORPP. The present design methodology is applied to an ill-conditioned plant for comparison with existing methods.