When terminating #14 or #12 stranded copper wire to a device, is it acceptable to merely wrap the strands around the terminal screw? How about the use of Sta-Kons?

We've all back twisted the strands of the wire and wrapped the wire around the terminal screw, and we've all used Sta-Kons, but are these methods really approved? Even though I've used these methods for years, both seem a little hokey to me. Many devices do not have the room for the Sta-Kons, and can break easily when the terminal is tightened, and the back twisting method seems like it could very easily let go.

Some devices seem to be designed for stranded wire. The ones with the internal clamp behind the terminal screws. This seems like the only really good method of terminating stranded wire to a device.

Matt