Well in the world of amateur road racing, a lot of guys will buy the cheap race tires and have them shaved before even taking them to the race track. The reason being if the tire only has 4/32" of tread instead of 8/32" of tread, the treadblocks don't "squirm" as much during cornering and they're generally a lot more predictable. I can only guess that brand new tires with full treadblocks move around a lot more and thus generate more friction than very worn tires with extremely short treadblocks. It would make sense to me that a very worn tire could have lower rolling resistance than a brand new one.

Uh oh... could this be the start of a new trend? Hypermilers having their tires shaved down to half-depth before even having them mounted up?