This chapter explores the minimum-based detector, for the Pareto Type I clutter case, in more detail. The minimum-based order statistic detector has been shown to perform very well in cases where its threshold multiplier is not too large. Saturation issues tend to occur when the Pfa is smaller than 10-2 and the size of the Clutter range profile (CRP) exceeds 2. Detector saturation is a term used, in the context of sliding window decision rules, to describe the situation where the normalised measurement of clutter is so large that the Cell under test (CUT) never exceeds it. This means that in simulated performance, the detector returns a probability of detection of zero for every signal to clutter ratio (SCR). False alarm regulation analysis of the new minimum can be performed very simply since it is possible to derive a simple closed form expression for the resultant Pfa during clutter power transitions.