  A pinnacle of a permutation is a value that is larger than its immediate
neighbors when written in one-line notation. In this paper, we build on
previous work that characterized admissible pinnacle sets of permutations. For
these sets, there can be specific orderings of the pinnacles that are not
admissible, meaning that they are not realized by any permutation. Here we
characterize admissible orderings, using the relationship between a pinnacle x
and its rank in the pinnacle set to bound the number of times that the
pinnacles less than or equal to x can be interrupted by larger values.
