* U.S. ISM non-manufacturing index rises in September
* U.S. private-sector payrolls top expectations
* Focus on U.S. non-farm payrolls (Repeats to additional subscribers without any changes to text)
NEW YORK, Oct 4 (Reuters) - U.S. Treasury debt yields drifted higher on Wednesday after a measure of U.S. services sector activity hit a 12-year high, offsetting some concerns about an upcoming payrolls report.
Yields took off after data showed that the U.S. non-manufacturing index as measured by the Institute for Supply Management rose to 59.8 last month from 55.3 in August. The consensus expectation was for a reading of 55.5.
U.S. long-dated yields, which move inversely to prices, hit session highs after the data. But by mid-afternoon, yields came off their peaks.
"This could just be a little bit of a clean-up," said Tom Simons, money market economist, at Jefferies in New York. "My sense is that there are a lot of shorts out there, but there wasn't enough selling to push yields a lot higher, so some guys started to cover a little bit."
Yields were lower for most of the morning session prior to the ISM data, pulled down by uncertainty surrounding the upcoming U.S. non-farm payrolls report. That data was expected to reflect hurricanes that hit the United States last month.
"The level of uncertainty surrounding payrolls has been high," said Bruno Braizinha, interest rates strategist at Societe Generale in New York. "Economists find it hard to understand the effects of the hurricane on payrolls."
Wall Street economists expect just 90,000 new U.S. jobs for September, down from 156,000 in August, according to a Reuters poll.
Jefferies' Simons said many investors believed Friday's payrolls would be distorted in some way by the hurricanes.
"So I don't know if there are many folks out there looking at this payrolls number for direction," he added.
A report by payrolls processor ADP on Wednesday showed that U.S. private employers added 135,000 jobs in September, exceeding economists' expectations despite Hurricanes Harvey and Irma significantly impacting smaller retailers.
The jobs gain reported by ADP though was the smallest monthly increase since October 2016.
Aaron Kohli, rates strategist at BMO Capital Markets in New York pointed out that it is difficult to determine what the ADP number implies about Friday's jobs report.
"The on-consensus (ADP) read leaves the market still expecting a soft non-farm payrolls due to hurricane effects," he said.
In late trading, the benchmark 10-year U.S. Treasury note yield was at 2.333 percent, up from 2.332 percent late on Tuesday, while the 30-year yield was at 2.877 percent, compared with Tuesday's 2.872 percent.
U.S. two-year note yields were up slightly at 1.479 percent. (Reporting by Gertrude Chavez-Dreyfuss; Editing by Meredith Mazzilli and Cynthia Osterman)