The motivation for this paper came from analyzing the space-complexity of x-fast tries. All the sources I read, including Willards original paper, claimed that an x-fast trie takes space, where is the set of stored elements and is the number of bits needed to disambiguate the elements of . However, my intuition suggested that this bound isn’t tight because the prefixes are shared at the top of the x-fast trie. I set out to determine a tight bound for the space complexity. That was given by ,