(Adds analyst comment, byline, updates yields)

By Gertrude Chavez-Dreyfuss

NEW YORK, July 2 (Reuters) - U.S. Treasury two-year

yields slipped on Wednesday after data showed an unexpected drop

in private-sector jobs last month, cementing the chances of a

rate cut from the Federal Reserve at least at the September

meeting.

U.S. two-year yields, which track interest rate expectations,

were slightly down at 3.77%. The benchmark 10-year

yield, on the other hand, came off highs following the report,

and was last up 4.2 bps at 4.291%.

Private payrolls dropped by 33,000 jobs last month after a

downwardly revised 29,000 increase in May, according to the ADP

National Employment Report. Economists polled by Reuters had

forecast private employment increasing 95,000 following a

previously reported gain of 37,000 in May.

"The ADP report increased the odds of a downside surprise in

Thursday's nonfarm payroll release," wrote Jeffrey J. Roach,

chief economist at LPL Financial in emailed comments after the

data.

"Investor jitters could be a catalyst for a drop in yields

tomorrow if the jobs report is weaker than expected. I expect a

weaker-than-consensus report, increasing the odds the Fed cuts

three times this year."

Futures tied to the benchmark fed funds rate lifted the

chances of a rate cut by the July policy meeting, pricing in as

much as a 27% chance of a July cut post-jobs data, according to

LSEG estimates. It was last at 24%, compared with a roughly 20%

just before the data release.

For the September meeting, the market has fully priced in a

25 basis-point rate decline.

(Reporting by Gertrude Chavez-Dreyfuss; Editing by Andrew

Heavens and Chizu Nomiyama )