Stirling permutations may be used to describe the sequences by which it is possible to construct a rooted plane tree with k edges by adding leaves one by one to the tree. For, if the edges were numbered by the order in which they were inserted, then the sequence of numbers in an Euler tour of the tree (formed by doubling the edges of the tree and traversing the children of each node in a left to ride order) is a Stirling permutation. Conversely, every Stirling permutation describes a tree construction sequence, in which the next edge closer to the root from an edge labeled i is the one whose pair of values most closely surrounds the pair of i values in the permutation.