Thanks Tom, I went to Tirerack, and while I couldn't find the specific Dunlop tire you mentioned, I did see the Dunlop Sport 5000 which is asymmetric in some aspect ratios. (www.tirerack.com/tires/images/dunlop/du_s5000.jpg)

I still don't see how one mold can make tires for the right and the left unless you ignore the fact that the tread will contact the ground in reverse orientation on the two sides of the car.

I took a strip of paper and rolled it into a circle. Pretending it was a right-hand tire, I marked a direction of rotation, an inside and outside edge.
When I move it to the left side, either the inside and outside edges are swapped, or the direction of rotation is reversed.

In the design of the tire they didn't shy away from "V" shaped groove patterns. Won't that predispose the tires on one side to hydroplane while the other side continues to grip? I guess mine is a case of a little knowledge being dangerous. I would expect tires with this design to put cars into spins, so I excluded it as a possible solution. I don't think I would like to be Dunlop's lawyer though, explaining to a jury why they designed tires that have different properties on different sides of the car.