In this note, analytical results are obtained for the minimum peak tracking error magnitude achievable by some finite settling time control systems in response to a step reference input. The limits of these results as the settling time approaches infinity are also obtained. These are of interest since they represent performance bounds which apply for any finite order LTI controller of a given configuration (i.e., one-parameter or two-parameter). These limiting results have been previously given only as the numerical solution to be obtained from an infinite linear program. The systems considered are one-parameter discrete-time SISO where the plant has one unstable pole and one nonminimum phase zero. The result for a two-parameter compensator for plants with one nonminimum phase zero is also presented.