Oil prices settled a few cents higher on Tuesday, enough to stretch their gains to a third session in a row.

Dollar weakness, persistent declines in output from members of the Organization of the Petroleum Exporting Countries, and a demand-boost from cold weather in the East offered support. An expected weekly rise in U.S. crude stockpiles and ongoing concerns over rising domestic production, however, also pressured prices.

April West Texas Intermediate crude tacked on 3 cents, or less than 0.1%, to settle at $62.60 a barrel on the New York Mercantile Exchange after tallying a rise of 2.6% over the past two sessions. May Brent crude the global oil benchmark, rose 25 cents, or 0.4%, to $65.79 a barrel on London’s ICE Futures exchange.

Two key influences, “the U.S. ramping up output, weather on the East Coast tightening short-term supply,” have offset each other, said Scott Gecas, senior strategic account executive at Long Leaf Trading Group. “The latest news is two-sided, but all eyes will be on the [Energy Information Administration petroleum supply] report” due Wednesday, he said. “We are extremely bullish above $64 with an upside target of $67,” for WTI. Data from the EIA are expected to reveal a rise of 2.5 million barrels in crude stocks for the week ended March 2, according to analysts polled by S&P Global Platts. They also forecast declines of  500,000 barrels for gasoline and 1.6 million barrels for distillate, which include heating oil.

Meanwhile, world stocks have been particularly volatile since a rout in early February, with oil broadly tracking their moves. “Oil and equities were trading very much hand in hand and basically equity markets were calling the shots in terms of direction and trading patterns,” said Bjarne Schieldrop, chief commodities analyst at SEB Markets. He expects in the short term this trend will continue and that the selloff in equities isn’t yet over.