* Crude prices drop but remain volatile after recent

Middle East tensions

* Job openings fall but above expectations

* ISM Services expansion slows for second straight month

By Chuck Mikolajczak

NEW YORK, May 5 (Reuters) - U.S. Treasury yields fell on

Tuesday, along with a decline in crude prices as there were no

fresh signs of escalation in the U.S.-Iran war, offering a

reprieve to recent inflation worries while investors digested a

flurry of economic data.

Washington said Iran had not breached a fragile ceasefire in

the Middle East conflict on Tuesday, following an exchange of

fire between the two sides the previous day as U.S. forces

attempted to force open the Strait of Hormuz.

U.S. crude fell 4.28% to $101.86 a barrel and Brent

fell to $111.09 per barrel, down 2.93% on the day,

although the recent skirmishes kept the declines in check.

Since the U.S.-Israeli war with Iran began at the end of

February, yields have steadily climbed as worries about higher

prices have dented market expectations for rate cuts from the

Federal Reserve this year.

"There's not enough big headlines really to move it too much

in one direction or another, we're still at levels we didn't

contemplate at the beginning of the year, before the U.S.-Iran

conflict, for sure," said JoAnne Bianco, partner and senior

investment strategist at BondBloxx Investment Management in

Chicago.

"It's a really big move since the beginning of March, so

we're just at a more elevated level. It seems like the odds are

that if we continue to have Brent crude go up $3 to $5 a day,

you can see our rates (rise), but that's also starting to make

fixed income more attractive, especially in the intermediate

part of the curve."

The yield on the benchmark U.S. 10-year Treasury note

fell 2.8 basis points to 4.418% after rising to

4.464% on Monday, its highest since March 27.

Several brokerages have scaled back expectations for rate cuts

from the Federal Reserve since the start of the year, when

markets were pricing in about 50 basis points of cuts for 2026.

The yield on the 30-year bond shed 2.6 basis

points to 4.999% after breaching the 5% level to hit 5.036% on

Monday, its highest since July 17.

Markets will receive several reports on the health of the

labor market this week, culminating in the government's jobs

report on Friday. Economists polled by Reuters forecast a 62,000

rise in nonfarm payrolls.

Data from the Labor Department on Tuesday showed job openings

were down 56,000 to 6.866 million in March but above the 6.835

million forecast of economists polled by Reuters.

A separate survey from the Institute for Supply Management said

its nonmanufacturing purchasing managers index dropped to 53.6

last month from 54.0 in March and slightly below the 53.7

estimate. A reading above 50 indicates expansion and this was

the second consecutive month that expansion has slowed.

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, was at a positive 48 basis points.

The two-year U.S. Treasury yield, which typically

moves in step with interest rate expectations for the Fed,

dipped 2.6 basis points to 3.936% after hitting 3.993% on

Monday, its highest since March 27.

The breakeven rate on five-year U.S. Treasury

Inflation-Protected Securities (TIPS) was last at

2.790% after closing at 2.828% on Monday, its highest close

since August 2022.

The 10-year TIPS breakeven rate was last at

2.49%, indicating the market sees inflation averaging about 2.5%

a year for the next decade.