* Asian stock markets : tmsnrt.rs/2zpUAr4
* Asia shares mostly up, Europe to open shade firmer
* Bulls hope Fed Chairman Powell will sound dovish enough
* Dollar supported as Treasury yields edge up from lows
* Oil prices up as U.S. stockpiles fall
By Wayne Cole
SYDNEY, July 10 (Reuters) - Asian shares pulled ahead on Wednesday while rising Treasury yields lifted the dollar as investors waited anxiously to hear if the world's most powerful central banker would confirm or confound expectations for U.S. easing this month.
MSCI's broadest index of Asia-Pacific shares outside Japan advanced 0.4%, after three sessions of losses.
South Korea edged up 0.4%, but Japan's Nikkei lagged with a loss of 0.1%. E-Mini futures for the S&P 500 were flat, while EUROSTOXX and FTSE futures pointed to small opening gains in Europe.
Chinese blue chips barely budged as data showed inflation remained stubbornly subdued despite a spike in pork prices.
A worrying lack of inflation globally is one reason investors are counting on Federal Reserve Chair Jerome Powell to sound suitably dovish when testifying to Congress on Wednesday.
Futures are still fully priced for a 25-basis-point cut at the Fed's July 30-31 meeting, but have abandoned wagers on a half-point move. They had implied a 25% probability of an aggressive cut before Friday's upbeat jobs report.
"We still think the odds favour a 25 bps 'insurance' cut," said Kevin Cummins, a senior U.S. economist at NatWest Markets.
"The Fed's consideration of rate cuts is not only about growth but also about inflation, which remains well below target, and inflation expectations, which were breaking to the downside before the Fed signalled the likelihood of cuts."
Overnight, Atlanta Fed bank president Raphael Bostic let nothing out of the bag by saying the central bank was debating the risks and benefits of letting the U.S. economy run "a little hotter."
Lurking in the background, U.S. and Chinese trade officials held "constructive" talks on trade by phone on Tuesday, White House economic adviser Larry Kudlow said.
Wall Street had been duly circumspect on Tuesday, with the Dow ending down 0.08%, while the S&P 500 added 0.12% and the Nasdaq 0.54%.
The cooling in U.S. rate fever has seen bonds give back just a little of their huge rally, with yields on two-year Treasuries rising to 1.917% from the recent trough of 1.696%.
That in turn has helped the dollar bounce on a basket of currencies to 97.500 from a June low of 95.843.
The dollar also firmed to 108.90 yen, while the euro faded to $1.1206 having been as high as $1.1412 just a couple of weeks ago.
The Mexican peso was nursing a few bruises after sliding on Tuesday when the country's moderate Finance Minister Carlos Urzua suddenly resigned, citing "extremism" in economic policy.
The Canadian dollar was on the defensive ahead of a rate meeting by the Bank of Canada in case policymakers tried to slow the currency's recent rally.
The dollar's gains took the shine off gold, which eased 0.3% to $1,393.68 per ounce.
Oil prices were supported by Middle East tensions and news that U.S. stockpiles fell for a fourth week in a row, easing concerns about oversupply.
Brent crude futures rose 64 cents to $64.80, while U.S. crude gained 82 cents to $58.65 a barrel.
Editing by Jacqueline Wong & Shri Navaratnam