NEW YORK (CNN/Money) - Treasury prices edged higher Tuesday, and held near the day's highs, after finding renewed focus on economic uncertainty.

Treasury bond prices had retreated during the last few sessions as investors pulled money out of the safe-haven sector and put it into more risky but higher-yielding stocks, casting a vote that the war in Iraq is on its last legs.

Yet the end of Tuesday's sessions suggested a drop in stock enthusiasm, as investors took in the fact that regardless of when the war ends, the challenges of a struggling U.S. economy remain.

At around 4:00 p.m. ET, the benchmark 10-year note rose 10/32 of a point to 99-15/32, slightly lowering its yield to 3.94 percent from 3.95 percent late afternoon Monday. The 30-year bond added 24/32 of a point in price to 106-27/32 yielding 4.92 percent versus 4.96 percent in late trading on Monday.

The two-year note rose 1/32 of a point to 100-3/32, pushing its yield to 1.58 percent, while the five-year note added 7/32 of a point to 100-22/32, yielding 2.84 percent. Yields move inversely to prices.

U.S. forces bombed a Baghdad compound where it was believed that Saddam Hussein and his family may have been staying, and that revived hopes that the Iraqi leader might be dead. The building that Hussein and his sons were said to be meeting in was destroyed, but the men's whereabouts have not been confirmed.

"The ability of Treasurys to bounce even with speculation that Iraqi President Saddam Hussein might have been killed overnight "is somewhat noteworthy," said Michael Cloherty, Treasury market strategist at Credit Suisse First Boston.

The rumor-driven market has spent the first nearly three weeks of war jumping at any credible-sounding rumor. It seemed to take a more muted reaction to the latest "Saddam is dead" claim, perhaps due to increased fighting between U.S. forces occupying parts of the capital and resistance forces loyal to Saddam. (Click here for CNN.com's war coverage)

"I don't know whether he survived," President Bush said Tuesday at a press conference with British Prime Minister Tony Blair in Northern Ireland. "The only thing I know is that he's losing power ... Saddam Hussein will be gone."

The war news did not bolster the U.S. dollar despite the president's assurances that a new administration soon might be in place in Iraq.

The dollar bought ¥119.84, down slightly from ¥119.95 late Monday. The euro bought $1.0715, up from $1.0669 late Monday.