* U.S. to sell $30 billion new three-year notes * Fed's Rosengren sees gradual reduction of stimulus * U.S. trade gap shrank to smallest in four years in November * U.S. Senate confirms Yellen as Fed chair, as expected By Richard Leong NEW YORK, Jan 7 (Reuters) - U.S. Treasuries prices held steady on Tuesday with benchmark yields hovering near two-week lows ahead of a $30 billion auction of three-year notes, part of this week's $64 billion in coupon-bearing government debt. The bond market has stabilized early in the new year after a dismal 2013 as evidence of cooling in car sales and the services sector raised bets the Federal Reserve would pare its massive bond purchase program very slowly in the coming months. The U.S. central bank said last month it will buy $75 billion in Treasuries and mortgage-backed securities in January, $10 billion less a month than what it had been purchasing in its effort to hold down long-term interest rates and stimulate the economy. Fears about the Fed tapering its bond purchases resulted in the Treasuries market in 2013 recording its third biggest annual loss in 40 years. Now some investors are reconsidering seeing the Fed move as a shift in its accommodative policy tilt and reckon the current yield levels are an over-reaction to the tapering. "I'm paying attention to the tapering. They haven't stopped that. They are still trying to buy bonds to help increase economic growth," said James Barnes, fixed income portfolio manager at National Penn Investors Trust Co. in Wyomissing, Pennsylvania. On Tuesday, Boston Federal Reserve President Eric Rosengren said the Fed will reduce its third round of large scale bond purchases "only gradually" because the economy, while improving, remains fragile as price growth remains too low. Rosengren, who is not a voter on the policy-setting Federal Open Market Committee this year, was speaking at an event to a business and industry group in Hartford, Connecticut. The Fed will buy $2.25 billion to $3.00 billion in debt due in February 2021 to November 2023 at 11 a.m. (1600 GMT), which is part of its planned $40 billion purchases in Treasuries in January for its QE3 program. In other Fed developments, the U.S. Senate as expected confirmed late Monday Janet Yellen to replace Ben Bernanke as chair of the Federal Reserve, making her the first woman to lead central bank in its 100-year history. For Wall Street, her leadership should mean the Fed's stimulative policies will continue in a bid to bolster an uneven recovery saddled with relatively high unemployment and low inflation. Still, the economy has proven resilient. The Commerce Department said on Tuesday the U.S. trade deficit shrank to a four-year low in November on record exports. Benchmark 10-year Treasuries notes were little changed in price at 98-6/32 to yield 2.960 percent. On moderate volume, the 10-year yield fell to a two-week low of 2.943 percent earlier Tuesday. It rose to a near 2-1/2-year high of 3.041 percent last Thursday, according to Reuters data. HEAVY SUPPLY WEEK Investors, while awaiting the Fed's minutes on its December policy meeting on Wednesday and the government's payrolls report on Friday, prepared to make room for this week's heavy supply of public and private bonds. The Treasury Department will hold a $30 billion auction of three-year debt at 1 p.m. (1800 GMT). It will sell $21 billion in 10-year notes on Wednesday and $13 billion in 30-year bonds on Thursday. In "when-issued" activity, traders expected the upcoming three-year issue to sell at a yield of 0.8060 percent, which would be the highest yield at a three-year auction since September. Investors and analysts forecast solid demand for the three-year notes given the relatively wide yield gap between two-year and three-year Treasuries, but they were less certain about the bidding for longer maturities before Friday's payroll data. "It's an opportunity to pick up some yield," National Penn's Barnes said. The three-year yield was 36 basis points above the two-year yield early Tuesday, compared with 31 basis points a month ago and 12 basis points a year ago . Competing for investors' cash will be an expected flood of investment-grade corporate bonds. Wall Street underwriters forecast that companies plan to sell $90 billion to $100 billion in high-grade debt in January, according to IFR, a unit of Thomson Reuters.