Throwing one away

Why would you have an ordering that isn't stable? The obvious answer is that a hash table with chaining is commonly used and does not reliably provide a stable order (as collisions tend to be ordered based on creation order).

My preferred mechanism for directory indexing is a hash table with internal chaining. It easily provides a reliable fixed size telldir cookie, and performance should be quite good until the number of directory entries gets to about half the cookie space.