wordsandwich

I adore word games. My current obsession is wordsandwich.
In this game, you zoom in to a specific 5-letter word by typing words and seeing if your guess is alphabetically before or after the word.
Starting with MYTHS (as close to the middle of the alphabet as you can get), I initially use a binary search, continuously splitting what's left of the alphabet in half.
Still, the last steps are the trickiest and I usually can't crack it in under 14 steps. Can you do better?
Note: switch off the groovy lounge soundtrack if it bothers you. And it will.