We have Dunlop Direzza DZ03s on the Supra, which are road legal track tyres, which are probably the best its had as it would always spin when pulling away before (driving normally it was still struggle for traction) but when these are warm she sticks to the road like glue, although rain is another story, but she only ever goes out when its dry (greasy roads last weekend was interesting lol).
Worst thing about them is the price £350 each!!
http://www.tyrereviews.co.uk/Tyre/Dunlop/Direzza-DZ03.htm