No tricks. Don't oversoak them. I like to keep them in a 35mm film cannister. The straw things would work too.
Actually, I prefer to keep a tiny travel size vaseline (small tube, like a toothpaste tube about half the size of my thumb) and a couple of tampons. There's a TON of cotton in one of those. Not sure how many cotton balls it's comparable to, but it's a bunch.
You also can use them as bandages. Believe it or not, those things do a great job plugging a hole and soaking up blood. Serioiusly. They do. If fire isn't a concern, you can use the vaseline for first aid purposes (chapped lips etc). I'm really into multiuse.
I'd also add steel wool. It's da bomb when you accidentally doused your firekit.
Fatwood is ok, but I rarely carry it. I also rarely carry matches. Four to six waterproof matches are as large as a bic. Frankly, I've never had a bic fail on me. The firestarter is just a backup which I like to play with.
Also, spend some time learning which naturally things in your area burn well. Barks, fungi, etc. You should be very familiar with them. Knowledge is THE BEST survival kit.