Hey, the pieces of fret wire that sandwich the 12th fret on my guitar (an epi LP) recently somehow got indents in them (after the 12th fret maker, under the d, g, and b). My strings get caught in the dents/nicks when I do bends on that fret. How do I fix this?

Can I just remove the strings and carefully use an emery cloth to smooth out the fret wire, or does it require a more specific procedure? Thanks.
I'd say it depends on how bad the fret wire is dinged up - if it's bad, no amount of buffing will fix it. If that's the case, best to take it to a luthier and see what they say.

Have to be pretty light to get them out, and bear in mind that you'd actually be lowering that fret, so the string may fret out against frets closer to the end of the neck.

How'd the wires get dinged up?? Just through playing?
It's not that bad or deep, it's just enough so that the strings catch on the dents. I'm not too sure how the wires got the dents in them, I guess it's just one of those mysterious guitar damages. Hmm...
That'll happen 1 of 2 ways. 1, you played a tapping lick too hard. 2, the guitar was dropped and the fretboard took the hit, which caused a string to dent the fret.

On the plus side, if it's not that bad/deep, it's not an expensive fix. You just need to find a tech in your area that can do a fret level. This will take the nick out of the problem fret, then re-level all the other frets to make the guitar perfectly playable.
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