NEW YORK (CNN/Money) - Treasurys mustered small gains Tuesday but failed to recoup most of their losses from the previous session, when yields hit their highest levels in seven months.

At around 4:15 p.m. ET, the benchmark 10-year note rose 1/2 of a point in price to 95-26/32 for a yield of 4.15 percent, down from 4.21 late Monday afternoon. The 30-year bond gained 15/32 of a point in price to 104-21/32 yielding 5.06 percent, down from 5.09 late Monday.

The five-year note gained 1/4 of a point to 98-7/32 with a yield of 3.03 percent, and the two-year note rose 1/8 of a point to 99-6/32 with a yield of 1.55 percent. Bond prices and yields move in opposite directions.

As equities have remained strong and fears of deflation have eased somewhat, bond prices have begun to slide in recent weeks.

But bonds moved higher early Tuesday after the previous session's sharp declines as some traders bought on the dip.

"We're up because we went down so much yesterday; that's about it," Vincent Verterano, head government bond trader at Nomura Securities, told Reuters.

But other traders said some potential buyers stayed on the sidelines, nervously awaiting new supply. The Treasury will sell $25.0 billion in two-year notes on Wednesday and next week will announce the terms of its multibillion early August quarterly refunding auctions.

Monday's sharp declines, raising yields to seven-month highs, came on the back of a shift in sentiment over the past month as dealers, anticipating the end of a lengthy bull market in bonds as evidence of a strengthening economy grows, dumped Treasury securities.

Federal Reserve Chairman Alan Greenspan was fairly upbeat about the economy's prospects and characterized the chance of deflation as remote during his Congressional testimony last week. Bond investors worry that the pace of economic growth will soon pick up, thereby pushing rates higher and possibly causing a pickup in inflation.

Inflation is a bond investors' worst enemy since it erodes the value of long-term, fixed-income investments.

In addition, effects of the tax stimulus package are starting to set in, according to traders. Tax break checks were scheduled to go out to many families this week.

Meanwhile the dollar moved higher following confirmation that two of Saddam Hussein's sons were killed during a shoot-out with U.S. forces in the northern Iraq city of Mosul.

The euro bought $1.1338, down slightly from $1.1347 late Monday. The dollar bought ¥119.11, up from ¥118.46 late Monday.

"Clearly the news of the possible death of Saddam Hussein's sons has a pull on emotions for people in the markets, but it has been some time now since currency markets were really trading on the back of geopolitical developments," Andrew Weiss, a strategist with AIG Trading Group, told Reuters.  

--Reuters contributed to this report.