I don't think any cover of Tom Waits is better than the original, but this cover at least measures up to the ethos:
https://www.youtube.com/watch?v=i3ce7uDRo28
Fairly certain the guitar isn't plugged into anything
Singer missing the appropriate amount of teeth
The words are mostly there, and when they aren't it's close enough
Fret buzz doesn't even phase the guy
This is the true cover of Waits because the songs are supposed to come from unfiltered humanity. There are so many covers of his that feel like they can improve on the original with slick production, funky arrangements, **** that. Unless it's a hobo singing with a missing limb, it ain't Waits.