And there were so many of them! Then I saw this "Omi Brotherhood Menturm Medicated Stick with Menthol". It was made in Japan, and on the package it said it was for "dried, chapped and cracked lip". I had to give it a try.
I had been buying some and bring them back to the U.S. every year since then. It's "thick" and larger in diameter than standard stick lip balms, not too hard or soft, and it moisturizes and "stays" on your lips very well!
Oh, and it doesn't get all melty in my pocket! That's always a bonus.