NEW YORK (AP) — Stocks downshifted on Tuesday, a day after their powerful worldwide rally, but optimism remained high that the global economy may still be headed for a return to normal.

It was the second straight day that rising hopes for a COVID-19 vaccine pushed investors to reorder which stocks they see winning and losing, and the continuing revamp left the majority of U.S. stocks higher but indexes mixed. Treasury yields and oil, meanwhile, held onto their big gains from a day earlier or added some more amid strengthened confidence in the economy.

The S&P 500 dipped 4.97 points, or 0.1%, to 3,545.53, after erasing most of an early loss. The relatively small movement, though, belied a lot of churning underneath. Nearly two out of three stocks in the index climbed, while losses for some of the largest and most influential technology stocks offset them.

The Dow Jones Industrial Average gained 262.95 points, or 0.9%, to 29,420.92, and the Nasdaq composite dropped 159.93, or 1.4%, to 11,553.86.

The flashpoint for all the moves was Monday's announcement from Pfizer that a potential COVID-19 vaccine it's developing with German partner BioNTech may be 90% effective, based on early but incomplete test results.

"This was such an environment of exuberance, which makes sense given some pretty compelling statistics" about immunity response for the vaccine candidate, said Kristina Hooper, chief global market strategist for Invesco. "But there are still a number of steps between now and distribution."

Stocks of smaller U.S. companies, which tend to move more with expectations for the economy than their bigger counterparts, rallied again. The Russell 2000 index of small-cap stocks gained 31.97, or 1.9%, to 1,737.01 and finally climbed back above where it was in January. It's just 0.2% below its record high, which was set in 2018.

Several areas of the market that got beaten down through the pandemic and whose low prices make them look like potentially better values led the way. Energy stocks in the S&P 500 rose 2.5% for the best gain among the 11 sectors that make up the index, for example, though they're still down nearly 44% for 2020.

"We're seeing a continuation of this value trade that really took off in earnest yesterday," said Brian Price, head of investment management for Commonwealth Financial Network. "We're seeing follow through today, which is good news for those who have maintained a diversified portfolio."

But he said there needs to be more economic growth for a sustained recovery by many of the companies and sectors beaten down by the virus pandemic.

The Big Tech stocks that carried the stock market through the pandemic, meanwhile, are suddenly facing more scrutiny for their high prices. Their stocks soared through 2020 on expectations they'll continue to thrive if the economy is in lockdown mode. But that's left their prices looking too expensive to critics, even after accounting for their huge profits.

Amazon, which is one of those Big Tech stay-at-home winners, fell 3.5%. It also is facing antitrust charges filed by European Union regulators on Tuesday that accuse it of using its access to data to gain an unfair advantage over merchants using its platform.

Microsoft fell 3.4%, and Facebook lost 2.3%. Those drops have outsized effects on the S&P 500 because they're some of the largest companies in the index by market value.

The S&P 500 is already up 8.4% in November so far. Not only are hopes for a coronavirus vaccine helping to lift markets, so is clearing uncertainty about who will control the government next year.

Democrat Joe Biden over the weekend clinched the last of the electoral votes needed to become the next president. Republicans, meanwhile, appear likely to keep control of the Senate.

That's a "Goldilocks" scenario for many investors because it could mean low tax rates and other pro-business policies remain, while a more stable and predictable set of policies comes out of the White House. More than anything, though, a Biden win would wipe out the uncertainty that dogged the market through the long, vicious fight for the White House.

But analysts warn many risks still hang over the market, which could easily upend all the gains made in the last couple weeks.

The biggest may be whether investors have become too convinced about a potential COVID-19 vaccine. While early results are encouraging, no vaccine is about to go on the market, and there's no guarantee that one will or the timing of it.

Coronavirus counts, meanwhile, continue to surge at worrying rates across Europe and the United States. It's troubling enough in Europe that several governments have brought back restrictions on businesses.

And uncertainty could easily swamp Washington again. President Donald Trump has refused to concede and is blocking government officials from cooperating with Biden's team. Some Republicans, including Senate Majority Leader Mitch McConnell, are rallying behind Trump's efforts to fight the election results.

The Republican control of the Senate that markets seem to be so heavily banking on also depends on the outcome of a pair of runoff elections in Georgia in January.

Still, optimism remains across markets.

The yield on the 10-year Treasury held steady at 0.95% and remains close to its highest level since March. Benchmark U.S. crude oil rose 2.7% to settle at $41.36 per barrel.

European markets rose, while Asian markets ended modestly higher.

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AP Business Writer Joe McDonald contributed.