* ADP private payrolls just short of expectations
* U.S. services sector readings show growth
* Energy shares rise for third session
* Indexes up: Dow 0.1 pct, S&P 0.2 pct, Nasdaq 0.3 pct (Updates to afternoon trading)
By Ryan Vlastelica
NEW YORK, Dec 3 (Reuters) - U.S. stocks rose modestly on Wednesday as energy-related shares rose for a third straight session and data pointed to improving conditions in the U.S. services sector, which makes up a majority of the economy.
Market moves were slight, with many traders looking ahead to a key meeting of the European Central Bank. Still, the Dow hit an intraday record and the S&P neared its own record, set last week.
The S&P 500 energy sector rose 0.7 percent, outperforming both the broader market and crude oil, which continued to struggle. Cimarex Energy was one of the S&P 500's top gainers, up 4.3 percent at $107.32. Diamond Offshore rose 3.1 percent to $31.29.
While the sector is on track for its third consecutive daily advance - and is up 2.8 percent over that period - it remains the only industry group to be negative for 2014.
"Energy is the undervalued sector of the market, but trying to call the bottom of oil prices is like trying to catch a falling knife. There's value to be had, but also might be some more pain along the way," said Joseph Quinlan, chief market strategist at U.S. Trust, Bank of America Private Wealth Management in New York.
A gauge of growth in the U.S. services sector rose more than expected in November even as its employment component dipped, according to ISM, while Markit's reading of the sector showed growth, though as a slower clip.
Markets reacted mutedly to data showing the U.S. private sector created 208,000 jobs last month, fewer than expected. The numbers, however, suggested a slowing global economy was having a limited impact on domestic activity.
Momentum is building for the ECB to launch a program of sovereign-bond buying to boost the bloc's struggling economy, with most signs pointing to March for a decision. The ECB meets on Thursday.
"We're looking for any stimulus, and are vulnerable to no additional actions being taken," said Quinlan, who helps oversee $330 billion in assets. "We'll feel more confident about global prospects if we have a more proactive ECB."
The U.S. Federal Reserve's Beige Book report of anecdotal information on business activity said U.S. economic activity continued to expand in October and November, with lower gasoline prices boosting consumer spending.
At 2:00 p.m. (1900 GMT), the Dow Jones industrial average rose 16.51 points, or 0.09 percent, to 17,896.06, the S&P 500 gained 4.97 points, or 0.24 percent, to 2,071.52 and the Nasdaq Composite added 14.98 points, or 0.31 percent, to 4,770.79.
Advancing issues outnumbered declining ones on the NYSE by 2,011 to 1,009, for a 1.99-to-1 ratio; on the Nasdaq, 1,634 issues rose and 1,028 fell for a 1.59-to-1 ratio favoring advancers.
The S&P 500 was posting 99 new 52-week highs and 2 new lows; the Nasdaq Composite was recording 115 new highs and 58 new lows. (Editing by Nick Zieminski)