In a previous paper, the authors have shown that a low-gain controller of the form C-epsilon (s) = Sigma(k=-n)(n)K(k)/(S -iomega(k)) is able to track and reject constant and sinusoidal reference and disturbance signal for a stable plant in the Callier-Desoer (CD) algebra. In this note, we investigate the optimal tuning of the matrix gains K-k of the controller C-epsilon (s) as the scalar gain epsilon down arrow 0. The cost function is the maximum error between the reference signal and the measured output signal over all frequencies and bounded reference and disturbance signal amplitudes. Closed forms for asymptotically globally optimal solutions are given. The optimal matrix gains K-k. are expressed in terms of the values of the plant transfer matrix at the reference and disturbance signal frequencies. Thus the matrices K-k can be tuned with input-output measurements made from the open loop plant without knowledge of the plant model. Although the analysis is in the CD-algebra, to the authors' knowledge the main results are new even for finite-dimensional systems.