West Texas Intermediate crude for July delivery the U.S. benchmark, rose $1.11, or 1.6%, to settle at $68.83 a barrel on the New York Mercantile Exchange. That was the highest front-month contract finish since Oct. 22, 2018, according to Dow Jones Market Data. August Brent crude the global benchmark, advanced $1.10, or 1.6%, to $71.35 a barrel on ICE Futures Europe. On Tuesday, WTI and Brent prices also settled at more than two-year highs after the Organization of the Petroleum Exporting Countries and its allies, known as OPEC+, agreed to stick to a timetable for gradually easing production cuts this month and next.

Most of Wednesday’s rise for oil was “driven by expectations that gasoline inventories will take a hit” in the latest supply data, and “anticipation that Americans, who stayed home last year, will be taking to the road again,” said James Williams, energy economist at WTRG Economics.

The Energy Information Administration will release its weekly supply report on Thursday, a day later than usual because of Monday’s Memorial Day holiday. The American Petroleum Institute will release its supply figures late Wednesday. On average, analysts expect the EIA to report a fall of 3.3 million barrels in U.S. crude inventories for the week ended May 28, according to an S&P Global Platts survey. They also forecast supply declines of 1.1 million barrels for gasoline and 1.6 million barrels for distillates.

On Nymex Wednesday, July gasoline climbed 1.1% to $2.1941 a gallon and July heating oil added 1.7% to $2.1071 a gallon. The question now is whether oil prices can hold their gains “amid strong demand, despite plenty of downside risk on the supply side,” said Robbie Fraser, global research & analytics manager at Schneider Electric, in a daily report.

Meanwhile, the timetable for the OPEC+ plan should bring an additional 700,000 barrels a day of supply onto the market in June, and a further 840,000 barrels a day in July, numbers that include the unwinding of additional voluntary cuts by Saudi Arabia, noted Warren Patterson, head of global commodity strategy at ING, in a note. “The market appears focused on the more constructive outlook for later this year, with OPEC+ of the view that the market will see significant stock drawdowns between September and the end of the year,” he said. Worries about the prospective return of Iranian crude to the market have faded a bit. A round of indirect negotiations aimed at bringing the U.S. back into the 2015 nuclear agreement and Tehran back into compliance, which would set the stage for reversal of U.S. sanctions reimposed by former President Trump, aren’t expected to produce a breakthrough in the near future.

While some diplomats had expressed hope that a deal could be reached ahead of Iran’s June 18 presidential election, an Iranian government spokesman on Tuesday said negotiators now expect to complete a deal in August when President Hassan Rouhani’s term ends, Bloomberg reported.

The oil market has already “baked in the return” of 500,000 to 1 million barrels coming back in the market from Iran this year, said Rebecca Babin, senior energy trader at CIBC Private Wealth, U.S. “If those barrels do not make their way back into the market, the supply deficit could exceed the 2 million barrels per day already expected from September through December.”