There's often discussion here of tires for the GTS. I've been through a lot of different ones and have generally been pleased with all of them though I'm not a particularly aggressive rider pushing the envelope...
I've run Heidenau snow tires for a number of winters and love them. Seemed only natural that I would give the K61 Racer tire a spin. On the pavement they are solid, track nicely and almost no wobble. And wear like iron. At nearly 3500 miles they don't seem to have worn at all. Other rear tires were ready to change at that mileage. They're not as "sticky" and surefooted as others I've used but are nice tires.
There is a big, BIG exception with these those. They pretty much suck off the pavement in gravel and dirt. None of the street tires are great in that environment but the Heidenau tire is noticeable worse.
I dropped the Vespa last weekend descending a steep, shale hillside and chalked it up to me not paying attention. You can read about it in VESPA DROP.
This past weekend I did some experimenting off the pavement to see whether it was me or the tires. I've come to the conclusion I'm not as big an idiot as I thought. You can read more details on the tires in VESPA OFF PAVEMENT.
I think my next tire will be the Kenda K761 -- more of a dual sport tread. Over the years I've put thousands of miles on gravel and dirt. Maybe it's time to try a tire for that too...