I'm in the Army and I agree with Cecil (LOL). But you chose your branch and now you gotta wear the (*****) headgear, right.
o Start with a new cover. The old one already knows its bad habits it's time to hang it up.
o Since it's wool you want to shave the fuzzies down to give it a crisp form for forming and make it look better. Use a pack of cheap AAFES brand razors. They nick your face up but they are perfect here. Spread the material and shave EVENLY be careful not to go too thin in places or too deep. Use something smooth and rounded to place underneath to make it firmer. Don't forget to shave the inside too this will make it better to form
o After you shave that puppy. Use a lighter sparingly to get those small places you missed. Then iron it flat on high heat.
o Soak it in water don't just get it wet and put it in on your noggin for shaping. Since its wet it will form better but it will shrink when it dries so you got to stretch the material a little as you go around
o Where you've made creases hit in with the iron again
o After you got it shaped spray hairspray on it. This will lock in the shape you formed. Put a small saftey pin in the flappy part to the brim to make sure it stays that way.
o Let your cover dry over night in the shape.
Always fold your head's dust filter the same way when you store it after use