Lexicographic probability systems (LPS’s) are representations of lexicographic expected utility (LEU) preferences, which were axiomitized by Blume, Brandenburger, and Dekel [1991]. LPS’s that satisfy the mutual singularity condition can be viewed as providing beliefs conditional on events with zero prior probability a la Renyi [1955]. However, this interpretation loses much of its appeal when the space of uncertainty contains redundancies. The problem arises acutely in the construction of higher-order LEU preferences because the space of first-order lexicographic beliefs will contain uncountably many redundant representations of the same preference relation. It follows that the mutual singularity condition lacks bite when it is imposed on higher-order beliefs. In this paper, we resolve this issue by showing that there is a standard Borel spaceof LEU preferences without such redundancies.