* Upbeat ADP jobs data support view on Fed tapering * U.S. 10-year yield rises to highest since mid-Sept * ISM services, new home sales, Fed's Beige Book on tap * Fed to buy up $3.50 billion in medium-term debt By Richard Leong NEW YORK, Dec 4 (Reuters) - U.S. Treasuries prices fell on Wednesday after a report showed private-sector hiring grew at its fastest monthly pace in a year, supporting the view the Federal Reserve would pare its bond purchases sooner than some traders have thought. The price decline pushed benchmark yields to their highest level since mid-September. Short- and medium-dated yields climbed to their highest levels in about three weeks. "The market is pricing in a slightly higher probability of a tapering in December or January," said Mike Cullinane, head of Treasuries trading at D.A. Davidson in St. Petersburg, Florida. Payroll processor ADP said on Wednesday U.S. companies added 215,000 jobs in November, compared with an upwardly revised 184,000 increase in October. Analysts polled by Reuters had expected a November gain of 173,000. Some analysts use the ADP data to adjust their forecasts on the government's payroll reading. Economists polled by Reuters forecast U.S. employers likely added 180,000 workers in November following a 204,000 increase in October. The U.S. Labor Department will release its November payroll report at 8:30 a.m. (1530 GMT) on Friday. Another report that supports the view the Fed would pare its stimulus program by early 2014 was a contraction in the U.S. trade gap in October stemming from record exports. On the open market, benchmark 10-year notes last traded 20/32 lower in price to yield 2.848 percent, up 7.5 basis points from late Tuesday. The 10-year yield touched 2.852 percent, the highest level since mid-September. Thirty-year bonds shed more than 1 point in price to yield 3.899 percent, up 6 basis points from Tuesday, while the two-year notes slipped 1/32 in price to yield 0.301 percent, up 1.6 basis points from Tuesday's close. The yield gap between two-year and 10-year Treasuries, which is a proxy on investors' view on U.S. growth, grew to 2.55 percent, its widest level since July 2011, according to Reuters data. Another month of solid job gain would support the view the Fed will trim its third round of quantitative easing program, known as QE3, which began a year ago and has involved $85 billion monthly purchases of Treasuries and mortgage-backed securities. On Wednesday, the U.S. central bank planned to buy $2.75 billion to $3.50 billion in Treasuries due in 2021 to 2023, which will be its latest QE3 purchase. The Fed is now seen by most analysts as likely to begin reducing purchases at its March meeting, but some think that could be brought forward to January, or even later this month, if employment data comes in strong. Other possible market-moving data include October new home sales data and November services sector activity from the Institute for Supply Management. While the spike in mortgage rates this summer has slowed the housing sector, domestic services industries, as well as manufacturers, have remained resilient despite sluggish job growth and consumer spending.