Iterative feedback tuning (IFT) is a data-based method for the iterative tuning of restricted complexity controllers. A "special experiment" in which a batch of previously collected output data is fed back at the reference input allows one to compute an unbiased estimate of the gradient of the control performance criterion. We show that, by performing an optimal filtering of the data that are fed back, one can minimize the asymptotic variability of the control performance cost and, hence, minimize the average performance degradation that results from the randomness of the data. The expression of the optimal filter is derived, and a simulation illustrates the benefits that result from using this optimal filter as compared to the use of the classical constant filter.