  Kitaev, Potapov, and Vajnovszki [On shortening u-cycles and u-words for
permutations, Discrete Appl. Math, 2019] described how to shorten universal
words for permutations, to length $n!+n-1-i(n-1)$ for any $i \in [(n-2)!]$, by
introducing incomparable elements. They conjectured that it is also possible to
use incomparable elements to shorten universal cycles for permutations to
length $n!-i(n-1)$ for any $i \in [(n-2)!]$. In this note we prove their
conjecture. The proof is constructive, and, on the way, we also show a new
method for constructing universal cycles for permutations.
