Self-optimizing control provides nearly optimal operation of process systems in the face of varying disturbances, where the inputs are adjusted to hold selected controlled variables (c) at constant setpoints. It is possible to have better self-optimizing properties by controlling linear combinations of measurements (c = Hy) than by controlling individual measurements. Previous work focused on selecting combination matrix H to minimize worst-case loss, that arises due to the use of suboptimal self-optimizing control policy. In this paper, we present a method for finding combination matrix H that minimizes average loss for local self-optimizing control. It is further shown that the combination matrix that minimizes average loss is superoptimal in the sense that it also minimizes worst-case loss simultaneously. The usefulness of the results is demonstrated using an evaporator case study.