Signs of a more stable oil market have emerged since the cartel members last held a regularly-scheduled meeting. Oil prices CLN6, +0.04% LCON6, -0.38%  have gained more than 30% so far this year. And both West Texas Intermediate, the U.S. benchmark, and Brent crude, the global benchmark, briefly traded above $50 on Thursday.

Global production is falling following a larger-than-expected weekly decline in crude supplies, according to a report from the American Petroleum Institute late Tuesday. The report comes as the number of active-drilling rigs have been in a steady state of decline and oil-company spending cuts, oil-and-gas sector bankruptcies, and recent outages in Africa and North America, have been supportive for crude prices.

“OPEC members are likely to be a little happier going into June’s meeting than they were in December,” Tom Pugh, commodities economist at Capital Economics, said in recent research note.

Oil prices have “surged by about a third since the start of the year,” he said. The “higher prices will have removed some of the pressure on [OPEC] to act to prop up prices.”

But that doesn’t mean major oil producers can sit back and relax when they get together. Oil market supply and demand haven’t fully stabilized and there a lot of factors than can, and probably will, rock OPEC’s boat.

Here’s a rundown of what analysts see as the key issues at hand and possible outcomes for the OPEC summit:

OPEC Headquarters in Vienna .AFP/Getty Images

“The market is eager to hear about a viable agreement between the OPEC producers and [non-OPEC] Russia to limit production,” said Dr. Ariel Cohen, a nonresident senior follow at the Global Energy Center at the Atlantic Council.

“This is a classic prisoner’s dilemma,” said Cohen, who is also an analyst at crowdsourced consultancy, Wikistrat. “Whoever starts to cut loses, because other members cheat.”

Saudi Arabia, Russia, Qatar and Venezuela said in February that they wouldn’t increase oil production above January’s levels, but only if other major oil producers followed suit. OPEC member Iran was very clear, then and now, that it will continue to raise its output to presanction levels before it’ll even consider such a move.

Major oil producers met again during a highly anticipated special meeting in April and failed to reach a deal.

The market really needs to freeze production, “in order to create a firm price floor and allow the oil price to gradually creep back upward,” said Dr. Justin Dargin, senior follow at the Oxford Institute for Energy Studies.

Read: It’s too early for the oil market to say farewell to oversupply

Market shareOf course, the biggest obstacle in getting a deal done to freeze output is market share.

“There are concerns that Saudi Arabia and Russia could increase output in the next few months to maintain market share as Iran ramps up its production,” said Pugh.

In April, Iran raised its daily oil output by 300,000 barrels a day to 3.56 million barrels a day, according to the International Energy Agency. That’s a level not seen since before sanctions on the country were tightened.

Read: ‘Iran oil came back at much faster than expected’: strategist

“Market share is market share and it is not in Saudi interest to make any meaningful concession on output that grants Tehran greater market share without significant concessions on other matters such as Syria, Yemen and similar,” said Thomas O’Donnell, a global energy analyst and a fellow at the American Institute of Contemporary German Studies.

“For now, there is no evidence that such deals are near at hand,” said O’Donnell, a Wikistrat analyst.

Saudi oil regime changeThe OPEC meeting will also be the first with Khalid al-Falih as Saudi Arabia’s oil minister.

Al-Falih, chairman of Saudi Arabia Oil Company, replaced longtime Saudi Oil Minister Ali al-Naimi earlier this month.

Read: Here’s what the departure of Saudi Arabia’s al-Naimi means for oil prices

“The appointment of a new energy minister is significant because it signals that Saudi Arabia, under Prince [Mohammed bin] Salman, intends to double down on its market-share strategy and commitment to low oil prices,” said Ravi Ramamurti, a distinguished professor at the D’Amore-McKim School of Business at Northeastern University.

Read: Meet Khalid al-Falih, Saudi Arabia’s new oil minister

Salman wants low oil prices for two reasons: “the economic motivation is to slow the pace of substitution of oil” and the “political reason is that lower oil prices make it easier for the Prince to administer hard medicine necessary to diversify away from oil,” said Ramamurti.

Last month, the Kingdom approved a long-term blueprint for economic reform, dubbed “Saudi Vision 2030,” and said it plans to make itself capable of living without oil within the next four years.

Read: 4 things Saudi Arabia’s economic reform plan says about oil

Even so, O’Donnell said “nothing of substance will change” with the appointment of the new oil minister. “The only ingredient of immediate interest to the market [in regard] to the June meeting is the apparently greater proclivity of Salman to take on the Iranians.”

OECD, IEA  Seasonal demand

Of course, there is a chance OPEC members can just leave the oil market to take care of itself.

The peak summer energy demand season is coming up, which will likely result in lower oil exports, said Dargin.

Soon, the market may see increased demand and reduced exports “leading to the oil price strengthening somewhat even without a production freeze,” he said. So “even without a workable production freeze created, there will be less oil on the market.”

Read: Is surprisingly strong gasoline demand a sign of what’s to come this summer?

‘Lipstick on a pig’ outcome?

With so many factors to consider, OPEC will have to collectively find a middle ground.

At least eight OPEC members favor a production cut, but those countries account for a bit less than half of the cartel’s output, according to James Williams, energy economist at WTRG Economics. “They would probably settle for a production ceiling.”

Kuwait, Qatar, Saudi Arabia and the United Arab Emirates have half have of OPEC’s production and “relatively strong financial but weakening portfolios,” he said. So at most, OPEC may put a cap on production, he said.

But O’Donnell said after the “market-diplomacy fiasco in Doha,” where all the talk ahead of that producers meeting pointed to a production freeze deal that never really happened, “it is not rational to expect any substantive change from OPEC in June.”

Helima Croft, head of commodity strategy at RBC Capital Markets, said Saudi Arabia may signal that there is nothing that will induce them to “pull production at any point or salvage a floor.”

Still, OPEC can “potentially try to put lipstick on a pig or try to dress it up by having some kind of statement that tries to bring people together,” said Croft.

–Sara Sjolin contributed to this article.