The price movements in the Treasury market were small, bringing prices one or two fractions of a point to either side of flat. Market strategists described the market as being 'on hold' until the results of the Federal Reserve's policy meeting are released on Wednesday afternoon. Volume remained thin due to holidays in Asia that kept some regular participants away from the market. "This most recent up move in yields seems to have calmed a little bit," said Gennadiy Goldberg, interest rate strategist at 4Cast, Inc., referring to Monday's selling. "I guess people have realized there's no sense in getting ahead of themselves before the Fed." The Federal Open Market Committee begins a two-day meeting on Tuesday. The policy statement and news conference by Fed chairman Ben Bernanke that are to follow will mark the start of a new practice of announcing policymakers' interest rate projections. Many market participants also see a chance that the Fed will announce a specific inflation target. But no one can guess exactly how the Fed will communicate these new pieces of information. "A lot of people are just waiting to see what exactly the Fed says and what comes out, just because there are so many possibilities that they can do," Goldberg said. Greece, meanwhile, was clinging on Tuesday to hope of a last-minute bond swap deal to avoid a messy default after euro zone officials sent talks back to square one by rejecting a final offer from the country's private bondholders. On the supply front, Treasury traders were preparing for the first of three Treasury auctions for the week, a sale of $35 billion in two-year notes, set for Tuesday at 1 p.m. (1800 GMT). Another $35 billion sale -- this time of five-year notes -- is set for Wednesday, while a $29 billion sale of seven-year notes will take place on Thursday. Celebrations of the Lunar New Year holiday will affect markets in China, Hong Kong, Singapore and South Korea this week. The 10-year Treasury note was last trading 1/32 higher in price and yielding 2.05 percent, down from 2.06 percent at Monday's close. The 30-year Treasury bond was last up 3/32 in price for a yield of 3.13 percent, close to its closing level on Monday.