(Updated in New York afternoon time)

* Fed funds futures price 55% odds of September rate hike,

down from 68% on Monday

* Treasury says coupon and floating-rate note issuance to

stay steady for at least next several quarters

* ADP report shows private payrolls rise 44,000 in July,

about 25,000 below expectations

By Karen Brettell and Colin Barr

NEW YORK, Aug 5 (Reuters) - Treasury yields fell on

Wednesday as oil prices dipped on hopes of the Strait of Hormuz

reopening while traders also focused on economic data

culminating in Friday's July employment report.

U.S. President Donald Trump said there was an "all-day

negotiation" on Tuesday with Iran, characterizing the talks

positively while also threatening to hit Iran "really hard" if a

deal is not reached.

A proposed deal between Iran and Oman would give Iran control

over ships entering the Gulf through the Strait of Hormuz, a

senior Iranian source and two regional officials told Reuters on

Wednesday, in one of the biggest concessions yet to Iran.

Yields have been whipsawed along with oil prices by

alternating bouts of hope and disappointment as a deal to end

the Iran war remains unresolved.

"The pattern we're getting on the energy prices is kind of a

range-bound channel, where when it gets too high the U.S. has

this incentive to de-escalate, and when it gets too low Iran has

the incentive to escalate again," said Ryan Swift, chief U.S.

bond strategist at BCA Research.

However, "if we just stay in that range over the next six to

12 months, I think what's likely to happen is we're going to see

overall core inflation drift lower," Swift said.

The 2-year note yield, which typically moves in

step with Federal Reserve interest rate expectations, fell 0.66

basis points to 4.187%, the lowest since July 20.

The yield on benchmark U.S. 10-year notes fell

1.23 basis points to 4.615%.

The yield curve between 2- and 10-year notes

steepened to 42.6 basis points.

Fed funds futures traders are pricing in 55% odds of an

interest rate hike at the Federal Reserve's September meeting,

down from 68% on Monday.

Concerns about an increase in longer-dated debt sales also eased

on Wednesday after the Treasury Department said it will hold its

coupon issuance and floating-rate note issuance steady for at

least the next several quarters.

"It's a positive for the rates market," said Gennadiy

Goldberg, head of U.S. rates strategy at TD Securities. "We're

not expecting auction size increases until the middle of 2027."

The Treasury also said that it continues to evaluate

potential future changes to its coupon and floating rate auction

sizes, a shift in language from its May refunding announcement

when it noted potential future increases to the debt sales.

Analysts said that may be a hint that it could reduce sales

of longer-dated debt to ease market pressures if long-end yields

rise too far.

Meanwhile, traders are waiting on Friday's highly

anticipated jobs report for July, which is expected to show that

employers added 80,000 jobs last month. The unemployment rate is

expected to stay steady at 4.2%.

Wednesday's ADP private employment report showed an increase of

44,000 jobs in July, down from 95,000 positions added in June

and about 25,000 jobs shy of expectations. Wages rose 4.4% from

a year ago.

Other data showed that the U.S. services sector maintained a

strong pace of growth in July, but strong demand is colliding

with supply constraints, driving up input costs for businesses.