* 10-year yield edges above 2 percent * U.S. services sector grew in January -ISM * U.S. stocks rally after previous day's sell-off * Private index on euro zone business hits 10-month high By Ellen Freilich NEW YORK, Feb 5 (Reuters) - U.S. Treasuries prices fell on Tuesday as a rebound in Wall Street stocks and data on European business activity that indicated improvement in the region's economy cut the appetite for safe-haven government debt, pushing benchmark yields back above 2 percent. Sentiment in European bond markets contributed to the move to riskier assets, as yields on Italian and Spanish sovereign debt fell, a day after a jump on worries about possible political shake-ups in the two countries. "Concerns about Europe reasserted themselves yesterday and that flight to quality caused a dramatic rise in Treasury prices," said Wilmer Stith, portfolio manager of the Wilmington Broad Market Fund. "Today calmer heads prevailed." Benchmark 10-year yields edge back up to just over 2 percent, as data on the U.S. economy added to pressure in the bond market. The Institute for Supply Management said its U.S. service sector index showed expansion in the sector in January, though the pace of growth slowed slightly. "The economy is improving," Stith said. "The ISM report was a little weaker than last month, but the employment sub-index was the highest in seven years. Because of that, 10-year Treasury yields went back to 2 percent." Stock prices rallied on Tuesday, further damping investors' ardor for safe-haven U.S. debt. Selling of long-dated hedges on debt securities known as power reverse dual currency notes also weighed on Treasuries prices. Dealers have been unwinding hedges on these "exotic" products due to weakness in the Japanese yen against the dollar, traders and analysts said. Benchmark 10-year Treasuries notes slipped 13/32 in price to 96-21/32, their yields rising to 2.01 percent from 1.96 percent late on Monday when 10-year yields hit a more than nine-month high. The 30-year bond fell 28/32 lower in price to 91-06/32. Its yield rose to 3.21 percent from 3.16 percent at Monday's close. The yield on 10-year Spanish government notes fell from Monday's six-week high to 5.38 percent, down 5 basis points, while the yield on Italian sovereign debt slipped to 4.46 percent, down 1 basis points from late on Monday. Some analysts pointed to signs the euro zone's economy may be turning the corner. Markit's Eurozone Composite PMI, which is based on business activity across thousands of companies, rose in January to a 10-month high of 48.6 from 47.2 in December - an improvement on the preliminary reading, though still below the 50 mark that delineates growth from contraction. On the supply front, the U.S. Federal Reserve bought $1.534 billion in Treasuries that mature between February 2036 and November 2042, part of its commitment to buy $44 billion in Treasuries in February. The U.S. central bank has been buying Treasuries and mortgage bonds in an attempt to lower borrowing costs and stubbornly high unemployment. The U.S. Treasury Department sold $45 billion in one-month bills, a record amount for this maturity. These one-month T-bills fetched an interest rate of 0.065 percent, compared with 0.035 percent on the $30 billion of one-month bills sold last week. EXOTICS MOVE The derivatives market showed signs of reduced demand for long-dated, fixed-rate payments in the dollar interest rate swap market, which some analysts said was due to dealers unwinding hedges on power reverse dual currency notes. Some Japanese investors have held these "exotic" but risky debt products, on which they received higher coupon payments when the yen was rising against the dollar. Since last fall, expectations the Bank of Japan would try to stimulate Japan's economy led the yen to weaken dramatically against the dollar. On Tuesday, the yen hit a 2-1/2-year low against the greenback at 93.51 yen, down about 21 percent from September, when speculation on the BoJ started. With the yen weakening, the coupon payments on these notes should fall, and dealers who sold these notes will likely need less long-dated cash payments to ensure they meet their coupon payments to investors, analysts said. The discount on the 30-year dollar swap rate to the 30-year Treasury bond yield, which narrows with lower demand for long-dated, fixed-rate cash flows, briefly narrowed to 15.25 basis points, a level not seen since March 2010. It then widened out to 16.25 basis points, unchanged on the day.