* U.S. 2-year note auction show strong results * Tuesday"s batch of U.S. data was better than expected. * U.S. 5-year breakeven rates hit highest since January 2004 (Adds new comment, auction results, update prices) By Gertrude Chavez-Dreyfuss NEW YORK, Oct 26 (Reuters) - U.S. Treasury yields were mixed on Tuesday in thin volume, with those on the long end of the curve falling for a third straight session, as investors looked to next week"s Federal Reserve meeting for clues on the timing of its first interest rate hike since December 2018. U.S. 10-year, 20-year, and 30-year Treasury yields all fell to one-week lows. A strong U.S. 2-year note auction, meanwhile, did little to drum up bids for the short end of the curve, as prices stayed lower. The auction posted a high yield of 0.481%, lower than the expected rate at the bid deadline, suggesting investors accepted a lower premium for the note. The bid-to-cover ratio, a gauge of demand, was 2.69, compared with an average of 2.50. A batch of better-than-expected U.S. data lifted short-dated note yields, flattening the curve, as investors priced in rate hikes by the Fed sooner rather than later. The spread between U.S. 5-year notes and 30-year bonds narrowed to 86.9 basis points. Tuesday"s data showed U.S. consumer confidence unexpectedly rose in October as concerns about high inflation were offset by improving labor market prospects. U.S. new home sales also surged, up 14% in September. "I think what is going on is that rate hike fears are being priced on the U.S. front-end at an accelerated pace," said Steve Feiss, managing director, fixed income, at broker-dealer Etico Partners. Further fanning earlier-than-expected Fed rate hikes is the surge in U.S. inflation. The U.S. 5-year inflation breakeven rate, which reflects inflation expectations over the next five years, hit another milestone on Tuesday, rising to 2.985%, the highest since at least January 2004. The 10-year breakeven rate also hit a milestone, climbing to 2.695% , its highest since May 2006. Fed funds futures are pricing in a 70% chance of a June rate hike on Tuesday, even though the U.S. central bank"s taper of asset purchases, if it begins in November, could end in June as well. Overall, rates futures traders are also betting on two rate hikes next year, the second one being in December. In afternoon U.S. trading, the benchmark U.S. 10-year yield was down nearly 2 basis points at 1.6185%. The U.S. 5-year yield, which reflects Fed tightening, was up half a basis point at 1.1828%. It touched an eight-month high of 1.193% last week. U.S. 30-year yields fell 3 basis points at 2.0506% . Jim Vogel, senior rates strategist at FHN Financial, said volume was thin for a third straight session on Tuesday, adding that the longer this runs, "the direction of the next sizeable move will grow in technical importance." October 26 Tuesday 3:24PM New York / 1924 GMT Price Current Net Yield % Change (bps) Three-month bills 0.055 0.0558 0.000 Six-month bills 0.06 0.0609 -0.002 Two-year note 99-158/256 0.4498 0.013 Three-year note 99-152/256 0.7637 0.011 Five-year note 98-136/256 1.1828 0.005 Seven-year note 98-156/256 1.4618 -0.005 10-year note 96-172/256 1.6185 -0.016 20-year bond 95-116/256 2.0299 -0.033 30-year bond 98-228/256 2.0499 -0.035 DOLLAR SWAP SPREADS Last (bps) Net Change (bps) U.S. 2-year dollar swap 17.25 0.00 spread U.S. 3-year dollar swap 16.00 0.00 spread U.S. 5-year dollar swap 8.75 0.00 spread U.S. 10-year dollar swap 3.00 0.25 spread U.S. 30-year dollar swap -19.00 1.25 spread (Reporting by Gertrude Chavez-Dreyfuss; Editing by Andrea Ricci and Sonya Hepinstall)