The new (introduced in 1997) 260 Remington that Woof mentioned is a very good cartridge. It is a 6.5 mm (.264 caliber) bullet stuck into a necked down 308 Winchester case. Not a 257 caliber.
Basically they duplicated the ballistics of a hand-loaded 6.5x55mm Swede Mauser using a 51mm long case instead of a 55mm case.
It seems to be pretty popular right now since it is used in short actions.
From a 260 Remington (6.5-308) you can expect (on average) from a 24 inch barrel:
85 grain= 3,400 fps
100 grain= 3,100 fps
120 grain= 2,800 fps
140 grain= 2,600 fps
160 grain=2,500-2,600 fps
I always wondered why they never necked the 308 case down to 257 caliber.
But then I started thinking that it has already been done in 1915 by Savage with the 250 Savage also known as the 250-3000. While it is a slightly shorter case than the 308. It is really the case (300 Savage) that inspired the 308 in the first place.
The old 250 Savage will give you:
60 grain= 3,500 fps
75 grain=3,300 fps
87 grain=3,000 to 3,100 fps
100 grain=2,900 fps
120 grain=2,700 fps
Not bad for a cartridge made to fire in a Savage 99 lever gun 94 years ago.