Best Way To Kill a Yellow Jacket Nest? (Update in the OP)

I'm aware of the gasoline method. I'm also considering some of this Spectracide stuff from Lowe's. If I can use a more organic method, though, I'd prefer to do it that way. Has anyone had any success using soapy water?

Whatever the method, death must come to them soon.

EDIT: Since I know you were all on the edge of your seats waiting for an update... I tried gasoline 2 days in the a row, but it didn't seem to have an effect on them. Doused the nest with an entire can of Spectracide, and that seemed to do the list. Still 2-3 errant flyers. And never did see a paper nest. Finally found the second entrance/exit to the nest, and there were way more of them than I initially suspected--dozens and dozens. Was very lucky two have gotten stung only twice after a ran the mower directly over one of the entrance point. Next door neighbors have two little girls who play a few feet away, as well.

If you're able to zoom in, you can see just how many there were (there were tons that didn't make it in the picture spread out further from the nest).

BTW, what are the bigger ones? Queens?