* Traders tweak positions ahead of Bernanke remarks * TIPS fare well after stronger-than-expected CPI * Fed's George wants to shrink QE3 right away * Fed buys $1.46 billion in bonds due 2036-2043 By Karen Brettell and Richard Leong NEW YORK, July 16 (Reuters) - U.S. Treasuries prices were a tad higher on Tuesday in advance of testimony before Congress from Federal Reserve Chairman Ben Bernanke which might offer clues on whether the U.S. central bank might reduce its bond purchases later this year. Bond buying was mild on below-average volume as traders sought to tweak their positions in anticipation of possible wild market swings from Bernanke's remarks on Wednesday, analysts said. The bond market was battered for about seven weeks after Bernanke hinted the central bank would consider paring its $85 billion of monthly purchases of Treasuries and mortgage-backed securities if the economic recovery continues its momentum. Benchmark yields rose to near two-year highs last week on worries the era of ultra-loose monetary policy was coming to end, although Bernanke and most Fed policy-makers have assured they plan to leave short-term interest rates near zero for a protracted period even if the Fed stops buying bonds. In the wake of those Fed comments and some weaker-than-expected data, bond yields have retreated from those peaks as bargain-minded investors stepped in and traders bought Treasuries to exit earlier short positions, analysts said. "The market has been whipsawed a lot lately and it's waiting for the chairman and whether he validates the idea about reducing stimulus. He has a tough job." said Robert Tipp, chief investment strategist at Prudential Financial in Newark, New Jersey. Bernanke is expected to reiterate at the two-day testimony before Congress, which begins on Wednesday, that the Fed will remain accommodative by holding rates low for a long time, even after it reduces stimulus by stopping bonds. Bernanke's testimony will be released at 8:30 a.m. (1230 GMT) on Wednesday. The consensus on Wall Street is the Fed will likely begin to scale back its monthly bond purchases in September. It will hold a two-day policy meeting at the end of July, then will meet again Sept. 17-18. The Fed bought $1.46 billion in bonds due 2036 through 2043 on Tuesday as part of its ongoing purchase program. "I think the central banks would like to get out of the bond-buying business and the way they are going to get out of it is by giving forward guidance that they are going to be extremely easy in the front end for a long period of time, which will anchor rates lower overall," said Tom Tucci, head of Treasuries trading at CIBC in New York. On Tuesday, Kansas City Fed President Esther George told Fox Business television the Fed should start paring its bond purchase program, known as quantitative easing or QE3, right away. In the cash market, 10-year Treasury notes last traded 3/32 higher in price with a yield of 2.532 percent, down 1.1 basis points and below the 2.755 percent set last Monday. The 10-year yield has risen nearly 1 percentage point since the beginning of May, according to Reuters data. On the Chicago Board of Trade, short-term interest rates implied traders factored in a 53 percent chance the Fed might raise rates at the end of 2014, slightly higher than a month earlier, before the June 18-19 Fed policy meeting. INFLATION STABILIZES Improving inflation data on Tuesday may bolster the case for less Fed stimulus after an earlier string of weak price readings raised the risk of deflation, which the Fed has also sought to avert through quantitative easing. The central bank, however, has downplayed concerns over falling inflation as temporary, saying it expects price pressures to rise back to its 2 percent target. The Labor Department said on Tuesday its Consumer Price Index increased 0.5 percent in June, the largest increase since February, after nudging up 0.1 percent in May, though gasoline prices accounted for about two thirds of that. "A lot of the categories of CPI follow the Fed's script to a large extent," including an increase in medical inflation, said Aaron Kohli, an interest rate strategist at BNP Paribas in New York. "The bounce back was very strong and I think that adds to their thesis that a lot of the softness is transitory." The rebound in price growth boosted Treasury Inflation Protected Securities, which were hammered during the May-June bond market selloff. The yield spread between 10-year TIPS and regular 10-year Treasuries grew to 2.12 percent, its widest level in about five weeks. The U.S. Treasury will sell $15 billion in a new 10-year TIPS issue on Thursday.