The "double" Davy knot is my favorite non-loop knot, and it's second only to the non-slip mono loop in strength for fly fishing tippet to fly knots. For more info on knot strength and the testing I performed, see my previous post. I call the knot the "extra-turn" Davy knot there, but I think "Double Davy" is a better name.
Here are pics on how to tie it. My previous post mentions this, but it's important to snug the knot mostly tight from both ends but then to pull only the standing end to finish tightening it. You'll hear and feel a little click when it's tightened properly.