A new technique has been proposed with some important advantages over the GLRT in solving composite hypothesis testing problems. CFAR fusion is one flavor from a menu of detection algorithms that arise from simultaneously applying an infinite number of likelihood ratio tests. We show that, when a universally most powerful (UMP) detector exists, it is always given by the CFAR fusion flavor. The GLRT is known to lack this optimality property. We also give examples where CFAR fusion is arguably a better solution than the traditional GLRT.