(Updates with market activity, analyst comment, auction details) By Ross Kerber June 8 (Reuters) - Traders on Tuesday sent longer-term U.S. Treasury yields to their lowest in more than a month after a report showed small business owners less confident, and narrowing the spread of a closely watched part of the yield curve. The benchmark 10-year yield was down 3.9 basis points at 1.5314% in afternoon trading. It reached as low as 1.513%, its lowest since May 7. Guy LeBas, chief fixed income analyst for Janney, said the dip seemed driven by the release in the morning of a survey from the National Federation of Independent Business showing small business confidence declined in May for the first time in four months. The theme was then reinforced by Labor Department data showing that U.S. job openings surged by nearly one million to a new record high in April. The report strengthened the view that a recent moderation in job growth was due to supply constraints. Thin liquidity contributed to the volatility, LeBas said. A midday auction of $58 billion of 3-year notes showed demand was "right on the market," according to an investor note from DRW Trading market strategist Lou Brien, with a high yield of 0.325%, little different than the note"s level at the bidding deadline. The morning"s bond buying pushed down a closely watched part of the U.S. Treasury yield curve measuring the gap between yields on two- and 10-year Treasury notes, seen as an indicator of economic expectations. It was at 138 basis points, about three basis points lower than Monday"s close, and had reached its lowest since May 7. The amount of money flowing into the U.S. Federal Reserve"s reverse repurchase facility was $497.428 billion, the second day in a row it hit a new all-time high and putting pressure on short-term interest rates. The 10-year TIPS yield was at -0.854% and the breakeven inflation rate was at 2.377% after touching its lowest since late April. The two-year U.S. Treasury yield, which typically moves in step with interest rate expectations, was down less than a basis point at 0.1527%. June 8 Tuesday 1:20PM New York / 1720 GMT Price Current Net Yield % Change (bps) Three-month bills 0.025 0.0253 -0.005 Six-month bills 0.0375 0.038 -0.003 Two-year note 99-242/256 0.1527 -0.004 Three-year note 99-216/256 0.3035 -0.009 Five-year note 99-230/256 0.7708 -0.022 Seven-year note 100-76/256 1.2055 -0.033 10-year note 100-220/256 1.5314 -0.039 20-year bond 101-216/256 2.1359 -0.034 30-year bond 103-136/256 2.213 -0.039 DOLLAR SWAP SPREADS Last (bps) Net Change (bps) U.S. 2-year dollar swap 7.00 0.00 spread U.S. 3-year dollar swap 10.75 -0.25 spread U.S. 5-year dollar swap 7.00 0.00 spread U.S. 10-year dollar swap -3.25 0.00 spread U.S. 30-year dollar swap -29.00 0.25 spread (Reporting by Ross Kerber in Boston; Editing by Will Dunham and Angus MacSwan) Our Standards: The Thomson Reuters Trust Principles.