The drop in longer-dated yields with 30-year yields touching a six-week low, pinned short-term gauges of Treasury market volatility near all-time lows.
"It was a quiet, firm day for the market. We have a pretty strong flattening trend that will probably continue into 2018," said John Canavan, market strategist at Stone & McCarthy Research Associates in New York.
Traders have favored longer-dated Treasuries over shorter-dated issues on expectations of further interest rate increases from the Federal Reserve and domestic inflation staying below the Fed's 2-percent target, analysts said.
Uncertainty about the passage of a Republican-sponsored bill to overhaul the federal tax code and diminished likelihood the government will introduce a Treasury bond that matures beyond 30 years have increased the appeal of "curve-flattener" trades, they said.
The two-year yield was a tad higher at 1.629 percent, while the 10-year yield slipped 1 basis point at 2.307 percent. This still narrowed their yield spread to just over 67 basis points, which was the tightest since November 2007, Reuters data showed.
The 30-year yield shed 3 basis points at 2.769 percent, a hair above a six-week low of 2.765 percent.
The latest three-year note supply enticed average demand from investors, resulting in the highest yield for this maturity at an auction since April 2010, Treasury data showed.
The Treasury Department will auction $23 billion in 10-year debt on Wednesday and $15 billion in 30-year bonds on Thursday.
Meanwhile, the curve flattening has coincided with the drop in short-term market volatility, which is a proxy of investors' confidence that inflation would stay low and the Federal Reserve will unlikely deviate from its gradual pace to raising short-term rates.
The CBOE 10-year US Treasury Note Volatility Index , which is seen as the bond market's counterpart to the VIX index for Wall Street, reached an all-time low of 3.55 on Friday before ticking up to 3.68 on Tuesday.
Another gauge of short-term bond volatility, the Bank of America Merrill Lynch one-month MOVE index, hit a record low of 45.05 on Monday.
"Inflation is tame and is expected to remain tame. You are going to see even lower volatility," Canavan said.