There is a small router bit available for Dremel tools that works. Very fragile bit, but if you are careful, it will wok OK.. In the dremel section of big box stores.
I have a Dremel carbide bit, but it's just slightly too big for 1/16". Maybe the one I have is for 1/8" line. I bought the smallest one available at Home Depot. I'll have to take a look when I get home.