Tapered barrel on HK rifles
 

The MR556 version of the hk416 has a tapered barrel.
Given that 556 is 5. 7mm in diameter, how small would the caliber reduction be... would the bullet be crushed to about 5. 5mm?

It's claimed to increase velocity but I don't known if that's due to a higher force behind the bullet, or literally because the bullet is slimmer when it leaves the muzzle (and thus has better ballistics)

A tapered barrel is tapered on the outside, not down the bore. Tapered barrels are offered to reduce the weight of the weapon, and don't usually effect the velocity of a round or it's accuracy. The bore size will always be uniform throughout the length of the barrel for any given chambering . The velocity of a round through a barrel is based on the cartridge you are using, the twist rate of the barrel, and the length of the barrel. Depending on the cartridge, longer barrels (tapered or untapered) usually allow rounds to achieve higher velocities and more rotation, which can improve accuracy of the bullet at longer ranges.

"swagged with a slightly smaller "INTERNAL" diameter at the muzzle end" is in the description for the HK MR556, apparently it actually is a tapered bore and not what all of us would associate with as a tapered barrel.
My buddy accidently loaded some .22 Hi power tips in .223/5.56 cases for his AR-15, he was happy with it touching holes at 100yds. until he realized that they were .227 diameter instead of .224.
They shot great and with no signs of pressure, I wouldn't doubt that if you checked multiple bores on rifles they could vary by several thousandth and not be of any consequence as for the bullet passing through them,

Thanks for the info, Grizzly - shows you're never to old to learn something new:)

I never heard of that either, like you stated, never too old to learn something new!