[irln]

I believe the rate is determined by the bidders at the auction and not by the Treasury.

https://www.treasurydirect.gov/instit/auctfund/work/work.htm

[igravious]

Exactly, otherwise Greece and other countries wouldn't have been locked out of the commercial markets if they could set rates. German rates were/are low because the German economy is thought to be a decent shape, Greek rates are high because the opposite.