The development of sliding window detection processes, based upon a single cell under test, and operating in clutter modelled by a Pareto distribution, has been examined extensively. This includes the construction of decision rules with the complete constant false alarm rate property. However, the case where there are multiple pulses available has only been examined in the partial constant false alarm rate scenario. This paper outlines in the latter case how the probability of false alarm can be produced, for a geometric mean detector, using properties of gamma distributions. The extension of this result, to the full constant false alarm rate detector case, is then presented.