Dry burns are your best friend. I only use an alcohol bath if a simple rinse and dry burn doesn't work.
If you use a brush you'll be surprised that it doesn't do much help. The material is bonded quite well to the wick, and the best method is to burn it off. I've tried to use a sewing needle to pick off some crud, but it doesn't work so swell.
The coil can take quite a beating from dry burning and I haven't had a coil break on me yet so don't be afraid of the coil breaking that way.