Butt splice connector to join 10 gauge to 12 gauge wire?

I'm no expert (far from it), but I have had wire nut connections fail. (Probably because I'm not an expert!!) Plus they are not waterproof, plus they result in a clumsy fat connection wrapped in layers of tape.

Having said that, there are sleek modern "waterproof" wire nuts -- don't know if they really work.

The most interesting part of this whole discussion, however, is this: Who knew that we could all get so excited about the different ways of joining two pieces of wire??