Rim Lighting with a Black Background - Help Needed

So this will be a very simple and short post!

I've been shooting some portraits with a black tablecloth background lately, and getting some really fun results with it. But, I'm running into one annoyance that I need to think through - my rim lighting from the rear of the subject is reflecting off of the subject and back onto my background, giving it too much variation in tone and color.

Here is what the set up looked like, with a little help from Lighting Diagram 

And here is the resulting image

How do I fix it, readers?