OIL firms find it hard to determine who their environmentalist adversaries are these days. They used to be easy to spot, with beards and dungarees. Now they spout forth corrupted Shakespeare to disrupt concert performances, or wear nuns’ habits at annual general meetings (AGMs). Increasingly others sport pinstripes, representing trillions of dollars of pension and other money.

As four of the five largest private oil companies prepare to meet shareholders next week, it is the green brigade in ties and suits that most worries them. At AGMs on May 25th CalPERS, the California state pension fund, with $294 billion of assets under management, plans to pressure ExxonMobil and Chevron, America’s two biggest oil companies. It wants the energy firms to outline risks to their business plans thanks to more-stringent-than-expected climate-change policies agreed in Paris in December. At ExxonMobil they will be joined by Norway’s Norges Bank Investment Management, the world’s largest sovereign-wealth fund, the New York City Pension Fund, global asset managers such as HSBC and BMO, which have about $650 billion of funds, and an ecumenical array of endowment-rich church groups.

Even Pope Francis will play a cameo role. The Sisters of St Dominic of Caldwell, New Jersey will invoke his encyclical about climate change in their proposal to commit ExxonMobil to support the Paris goal of limiting global warming to less than 2°C above pre-industrial levels.

ExxonMobil, the world’s largest private oil company, gives these resolutions short shrift. It argues that more energy is necessary to alleviate global poverty, and that technology—coupled with a carbon tax—will mitigate the environmental risks. It may hope that a recent rebound in oil prices to around $50 a barrel will pacify shareholders. But their frustrations have been fanned by a decade of wasteful spending in the oil and gas industry (see chart). Some believe that more restrained capital allocation would boost returns, as well as helping the planet.

Most, if not all, of the investors’ resolutions will fail, says Heidi Welsh of the Sustainable Investments Institute, an American research firm. Such is the relatively docile nature of owner activism in America. But she says pressure from investors, ranging from those with concerns about the long-term economic impact of climate change to those with more moral preoccupations, is “coming to a head”. This month, an unexpectedly high 49% of shareholders backed a resolution urging Occidental Petroleum, another American oil firm, to stress-test a two-degree scenario. Some 42% voted for climate-related resolutions at Anadarko, a rival, and AES, a utility. Robert McCormick of Glass Lewis, a proxy advisory firm, says such a large vote suggests that usually placid asset managers, such as mutual funds, may have joined the green revolt alongside pension funds—more established rebels. He notes that the resolutions, even if passed, would be non-binding. But if they are ignored, shareholders can express their frustration in subsequent years by refusing to support a company’s board nominees, he says. The pressure on the American supermajors follows the “Aiming for A” campaign by institutional investors in Britain that last year forced Royal Dutch Shell and BP, the biggest European oil firms, to agree to reveal how stringent climate-change policies would affect their investment portfolios. Change across the Atlantic has proved harder to effect. Anne Simpson of CalPERS says shareholders have weaker rights in America, which has a more litigious corporate culture and where it is harder to challenge boards than in Britain. She talks of a “shut up or sell up” mentality. Hence CalPERS is seeking “proxy access” at ExxonMobil that would give large shareholders the right to nominate board members. This is a growing trend in corporate America (a majority supported proxy access at Chevron last year), and Ms Simpson says it is aimed at installing a “climate-competent” board at ExxonMobil. The firm continues to reject it, even though last year the proposal gathered 49.4% of shareholder support. “If we can’t hold boards accountable we may as well sit and whistle,” she says, adding: “If we don’t win this year, we will be back next year.”

Yet even when firms agree to such resolutions, there is no guarantee their level of disclosure will satisfy investors. On May 11th Shell issued two reports on its assessment of climate-change risks in response to last year’s vote. Full of pretty pictures and snazzy charts, they revealed little about how climate policies would alter future plans for developing oil- and gasfields.

James Leaton of the Carbon Tracker Initiative, an investment-focused NGO, says that in one report Shell tried to downplay the role of private oil companies in generating greenhouse gases, seeking to shift the blame instead to national state-controlled firms with larger reserves. “We don’t need 50 pages of glossy documents,” he says. “Give us two pages and tell us what high-cost projects you would cancel.”

On the same day as the reports were published, Shell informed its employees that it was creating a “New Energies” business to invest in green technologies. But it and BP insist that hydrocarbons will still account for at least 75% of the world’s energy for decades to come. Their response to global warming is to promote natural gas over coal and, eventually, oil; renewable energy remains a tiny share of their investment budgets. “Rumours of the death of oil are a little premature,” says Peter Mather, head of BP’s British business.

The only supermajor that wins high marks from shareholders for what they say is a more committed response to climate change is Total SA, a French company, which like Shell hosts its AGM on May 24th. It plans to set out its ambition to develop an energy mix by 2035 consistent with Paris-style global-warming limits, including a pledge to invest $500m a year in renewables, and a “symbolic objective” to raise their share to 20% of its portfolio, from 3%. In an effort to complement its acquisition of SunPower, an American solar-energy company, in 2011, it launched an offer this month to acquire Saft, a French battery-maker, which will bolster its expertise in electricity storage.

But Total is likely to remain an oil and gas company above all else. Alongside its renewables aspirations, it claims that one of its most exciting ventures is producing natural gas in the pristine Russian Arctic. It does not see this as a contradiction. In fact, it argues that the focus on natural gas actually reflects its commitment to a two-degree global-warming scenario. From under their habits, French nuns may murmur growing disapproval in response.