* Wall Street opens slightly higher

* Oil prices climb after drawdown in U.S. supplies

* China data adds to global growth worries

* Dollar, U.S. treasury yields lower (Recasts, adds U.S. markets open, comment by analysts; previous LONDON)

By Elizabeth Dilts Marshall and Huw Jones

NEW YORK, Sept 15 (Reuters) - Global shares were off slightly on Wednesday as cooling inflation eased some fears of an early reduction in monetary stimulus, while a slowing economic recovery and uncertainty over higher taxes kept gains in check.

The MSCI All Country World Index was down 0.17%, and shares in Europe's STOXX index of 600 European companies eased 0.61%.

Data out of China showed that growth in its factory and retail sectors continued to falter in August with output and sales growth hitting one-year lows as fresh COVID-19 outbreaks and supply disruptions pointed to a possible economic slowdown in the mainland.

While U.S. data out this week shows inflation cooling and having possibly peaked, inflation in Britain was the highest in years.

Still, Wall Street indices rose on Wednesday, with the energy and financials sectors recovering some of their losses in recent sessions.

"The delta wave is likely receding in the U.S. and globally, and the pandemic recovery should restart," JPMorgan Securities analyst Marko Kolanovic wrote, referring to the highly infectious coronavirus delta variant.

"As delta subsides, and inflation persists due to supply frictions from reopening and accommodative monetary policy, we expect the reflation/reopening trade to resume its outperformance, and believe that bond yields and cyclicals likely bottomed early last month," Kolanovic added.

The Dow Jones Industrial Average rose 43.63 points, or 0.13%, the S&P 500 gained 7.61 points, or 0.17%, and the Nasdaq Composite dropped 5.90 points, or 0.04%.

Investors continued to scrutinize data on inflation after a report on Tuesday from the U.S. Labor Department showed it cooling. On Wednesday, data showing that U.S. import prices fell for the first time in 10 months boosted hopes that inflation may have peaked.

In contrast, inflation in Britain hit a more than nine-year high last month, though largely due to a one-off boost that analysts said was likely to be temporary.

All eyes now are on next week's U.S. Federal Open Market Committee's monetary policy meeting. Expectations that the Fed will announce plans to taper its bond-buying program were lower after Tuesday's softer-than-expected U.S. inflation data, especially as some expect inflation to remain high for months.

Possible increases to the U.S. corporate tax rate remain important in the background, and one bank estimated that raising the corporate tax to 25% could shave 5% off S&P500 earnings in 2022.

"We still have a very fragile market, especially if we get some type of tapering from the Federal Reserve," said David Wagner, portfolio manager at Aptus Capital Advisors. "Any material change to tax policy can create a more volatile market."

The dollar was last down 0.14%.

The yield on the U.S. government 10-year note was 1.2921%.

Oil prices rose more than $2 per barrel on Wednesday after industry data showed a larger-than-expected drawdown in U.S. crude inventories.

Brent oil was last up $2.32, or up 3.15%, at $75.92 a barrel. U.S. crude was last up $2.41, or up 3.42%, at $72.87 per barrel.

Spot gold fell $-10.6055 or -0.59%.

CHINA GROWTH WORRIES

After the Chinese data, Chinese blue chips were down 1%, and U.S.-listed Chinese stocks extended losses.

"This is not a dip, it is a falling trend that will last at least until the end of this year," Iris Pang, chief China economist at ING, said of the Chinese data.

Pang said she anticipates a 0.5 percentage point cut in Chinese banks' reserve requirement ratio (RRR) in October, and said more fiscal support is needed for small- and medium-sized companies.

Shares in property developer Evergrande, which is scrambling to raise funds to pay its many lenders and suppliers, fell for the third consecutive day on Wednesday, losing as much as 5.4% to their lowest since January 2014.

Hong Kong's benchmark Hang Seng index .HSI shed 1.8%, as casino stocks plunged after Macau began a public consultation that investors fear will lead to tighter regulations in the world's largest gambling hub.

An index tracking gaming stocks fell 23%, while Wynn Macau fell as much as 29% to a record low.

(Reporting by Elizabeth Dilts Marshall in New York, Huw Jones in London; Editing by Will Dunham)