Overall demand was solid, but interest from indirect bidders, a category that includes foreign central banks, was scant.
But investors did not seem to mind, with benchmark 10-year notes jumping 17/32 in price for a yield of 4.56 percent, down from 4.63 percent on Monday.
Bond bears failed to break a seven-month high near 4.70 percent last week, opening the door for at least a partial reversal of the market's fortunes.
That left investors with high hopes for this week's $44 billion refunding, although results of the first auction left a bit to be desired.
The new three-year debt was sold at a high yield of 4.458 percent and garnered 2.42 times the number of bids per dollar of debt on offer, well above a 2.23 average for the previous three sales of the same maturity this year.
But indirect bidders, often used as a proxy for offshore interest in Treasuries, bought only $5.26 billion, or 29.2 percent of the sale.
That was way below the 37.4 percent average in the prior three 2005 auctions and left primary dealers holding $12.12 billion, or 67.3 percent of the deal.
"The indirect bid was way below normal, so the foreign participation was not that great," said Frank Hsu, director of global fixed income at Fimat.
"Yet the market stayed higher, in part because it was oversold last week, having ignored bond-bullish data on jobs and labour costs."
The latest government payrolls data showed a labour market that was expanding at a very subdued pace, and a separate report on productivity suggested real wages were essentially stagnant and therefore were not generating inflation.
That data failed to have an immediate positive effect on bonds, but its ripples appeared to be helping the market this week.
Five-year notes climbed 9/32 for a yield of 4.48 percent, down from 4.55 percent on Monday. The 30-year bond surged 31/32 for a yield of 4.76 percent from 4.82 percent.
Five-year notes were up next in the refunding auction, with $13 billion up for grabs on Wednesday, followed by $13 billion of ten-year notes on Thursday.
Existing three-year notes were up 4/32 and yielding 4.44 percent, while two-year notes rose 2/32 for a yield of 4.42 percent, down from 4.46 percent on Monday.