BP's shareholders want to see some radical management action to help the company turn the page on U.S. oil spill litigation and the quarrel with its Russian partners.
Both issues have dragged on the value of a company that was once Britain's biggest, but which now languishes in sixth place with a tainted reputation in the two countries that together account for half its oil output.
A move to jettison the refining, petrochemicals and fuel retailing businesses that distinguish an "integrated" oil and gas company from one that just finds and produces the stuff is one potential step.
Another might be a bold takeover deal to deliver the big blocks of future output the larger players in the industry are struggling to find.
"The integrated model isn't delivering best value to shareholders. You look at Shell and Total and ENI - no-one has demonstrated that the integrated model works particularly well," said Stephen Thornber of Threadneedle Investments, a top 20 investor in BP.
"I would favor a much cleaner, much more upstream focused business which can utilise BP's exploration, development and production skills and reduce its exposure to the dilutive refining and petrochemical business."
U.S.-based ConocoPhillips this year spun off its refining and marketing arm to become the world number one pure exploration and production (E&P) company. Smaller Marathon Oil has done the same.
Refining assets - the main part of BP's business outside the dominant E&P or "upstream" side - can provide a temporary profit counterweight when crude prices are falling, and together with marketing they offer cost saving opportunities.
But many older refineries are distant from supplies and face competition from bigger, modern ones that are closer. In Europe and the United States in particular, where most BP refineries sit, players face regulatory and planning issues that make it tough to compete with new plants in India and the Middle East.
BP's "downstream" - refining, petrochemicals, lubricants and fuel retailing businesses - is profitable, but its 16 wholly and partly-owned refineries alone tie up $44 billion of capital.
The business is shrinking already and has been for over a decade. BP hopes to sell this year its Texas City refinery, another blot on its U.S. reputation after a 2005 explosion killed 15 people. It also plans to further reduce its 21,800 road fuel stations to help squeeze out $2 billion of cost savings this year.
Analysts estimate BP's refining business is worth about $20 billion, with marketing, lubricants and petrochemicals worth a further $14 billion - although in the current tough refining environment a buyer might be hard to find.
Another $25-$30 billion could become available if BP sells out of the Russian joint venture, TNK-BP it entered in 2003, as has said it is considering.
Such a move is by no means a certainty. BP's partners in the venture, a group of oligarchs whose uneasy relationship with the powerful Russian government and differing strategic vision for the business have hamstrung its activities, are not easy partners for any potential buyer.
BP has 29 percent of its production tied up in the business, and even if it does sell its 50 percent stake, there is every chance the cash will be ploughed back into Russia, the world's biggest oil producing country and number two exporter behind Saudi Arabia.
"If I was going to bet, I would say BP won't be leaving Russia," said a former BP executive with Russian experience. "Either there will be a new partner or it will get out (of TNK-BP) and recycle its investment elsewhere in the country."
On the other side of the financial equation stands a compensation settlement with the U.S. Department of Justice over the 2010 explosion on the Deepwater Horizon rig that killed 11 people and triggered the United States' worst offshore oil spill from the Macondo well in the U.S Gulf.
The parties are about $10 billion apart on a figure, with BP wanting to pay $15 billion and the DoJ holding out for $25 billion, according to a recent Financial Times report.
BP has already put aside about $3.5 billion, so a worst-case scenario has the company needing to find a further $21.5 billion.
But closure for BP on the oil spill episode would take a lot of pressure off its share price.
Thomson Reuters data shows BP shares trading at 5.2 times earnings per share. A recovery to the 6.7 times earnings, where European peers Shell and Total trade, would add $36 billion to its $125 billion market capitalisation.
Analysts who base their discount on tracking relative market value to pre-spill days say the potential for a value recovery could be much higher, at up to $70 billion.
If, as expected, the DoJ and BP hammer out a deal on spill compensation before U.S. presidential election in September, BP has a lot more money to play with.
Shareholders love a special dividend, but they love capital growth more.
"It's not going to be welcome as a buyer in the deepwater U.S. Gulf after what happened," said Robin Matthews, of JMW Energy Advisers, a division of auditors Deloitte.
"Onshore, you are looking at shale investment, and that's not the kind of high margin stuff they really want to be in. Where else can they really put that kind of money to work effectively?"
The answer could be in M&A, and what better fit than BG Plc - a gas-focused exploration and production company.
BG has the opposite problem from that of BP - plenty of projects and opportunities to pursue, but not enough funds.
The group has been shedding assets and issuing hybrid bonds in an effort to keep its best developments funded without stretching its balance sheet, and its long-serving chief executive, Frank Chapman, is due to retire in 2013.
"I am sure BG will be linked with them. They have some fabulous assets," said a second shareholder from among BP's 15 largest.
"The issue for BG is having enough cash to develop them all. So yes, I have heard sillier ideas. You do wonder whether Frank Chapman is looking for a big exit."
BG has been pitched as a takeover target ever since it was spun out of a former British state gas utility at the turn of the 21st Century but its high valuation could be difficult for a buyer.
In an industry where size means a lot, BG is in the small half of the Dow Jones oil and gas global titans index with a market value of $65 billion. But its shares trade at 13.6 times earnings - one of the highest in the index.
Whatever BP decides to do on the M&A front and with its downstream business, and whatever its fate at the hands of U.S. and Russian officials, shareholders want to see some action from Chief Executive Bob Dudley, the Russia veteran who took over after Tony Hayward fell on his sword for the oil spill.
"It's definitely true they are lacking strategic direction and they are running out of time to clarify that," said a third shareholder.
"If you have great assets, even if you make some appalling strategic errors - you'll most likely end up fine. So when Dudley can put Macondo and the Russian sale to bed, he will absolutely have the ammunition to create something brilliant."
© 2015 Thomson/Reuters. All rights reserved.