[TCML] Secondary with Carbonized Spots

[Derek Esq.]

Hey all, 
 
I've got an issue that I figure one or more of you has run into before. I have a small coil with a secondary that's about 8" tall that I inherited (not literally). It appears that there is no expoxy or anything coating the secondary. If there is, it's a very light coating. Somewhere nearer to the bottom of the secondary, there are two carbonized spots on the windings. The spots are slightly bigger than a spot made if you took a ball point pen and made a dot on a piece of paper. When I run the coil, I get arcs from the two carbonized spots to the primary. The coil runs fine otherwise with appropriate breakout from the topload. 
 
My question is, what can I do about these carbonized spots? Is there a way to repair them? If not, how can I prevent these spots from arcing over? Or what's the best option?
 
Thanks for all your help,
 
Derek