In some cases, they get naming rights. The Gulf of Mexico is peppered with fields named after geologists’ wives (risky if they are duds), or their favourite albums, bands, stars and football chants. They are part of the industry’s folklore. The question is, are they a dying breed?

Several prospective deals announced this month, from the deep waters of the Gulf of Mexico to onshore Iran, suggest that the industry may be shying away from expensive forays into uncharted territory, and taking a more cost-conscious approach to exploration and production. It remains to be seen whether they can maintain their discipline if oil prices recover. But, for now, “they’ve all gone back to the drawing boards,” says Andy Brogan, an oil-and-gas specialist at EY, a consultancy.

Days later some of the world’s largest oil companies, including BP, bid generously for exploration and production blocks in Mexican waters of the Gulf, which Mexico hopes could realise up to US$40 billion in deepwater investment from companies. Until 2014, private investment in Mexican oil had been banned since the 1930s, so there is a pioneer’s excitement about exploring for oil there. But it is also familiar territory, with some blocks lying just across the maritime border from America.

Adding to the sense of action, on December 7, Royal Dutch Shell, an Anglo-Dutch firm, signed a preliminary memorandum of understanding to develop oil in Iran, despite Donald Trump’s hostility to Barack Obama’s nuclear deal and the possibility of renewed sanctions. It followed a similar deal between Iran and France’s Total last month.

Such forays show that, for the first time since oil prices plunged in 2014, Big Oil is putting its head above the parapet to seek substantial new sources of crude that will tide it through the 2020s. It comes days after OPEC, a producers’ cartel, struck an agreement to rescue oil prices, which executives say has bolstered confidence that the market is stabilising.

Yet these bullish signals have not brought cheer to the elephant hunters. For years the industry has struggled to cover its investment needs and dividend payments (see chart). It barely broke even in 2012-14, though oil prices at times exceeded US$100 a barrel. Now, at half that price, it is having to scrape the barrel to satisfy shareholders who rely on its dividends. The result has been a historic plunge in oil-and-gas investment. It was a record US$780 billion in 2014. Since then it has fallen by about US$340 billion.

Oil executives say they are trying to embark on a new investment cycle without squandering money. Tim Callahan of BHP Billiton, an Australian oil-and-mining firm that won the bidding on December 5 for an US$11 billion project to develop the Trion field in Mexico with Pemex, the state oil company, says the aim is to be “fit at 50”, ie, able to make plenty of money at US$50 a barrel—or less.

The 60 per cent cut in the proposed cost of BP’s Mad Dog Two project suggests that there is plenty of fat to trim. Initially the company intended to install a state-of-the-art floating “spar” tailored, in the words of one official, like a “Savile Row suit”. That project was shelved in 2013.

The alternative is a standard “off-the-peg” version, though BP promises not to have compromised on safety. It will be the company’s first new platform since its Deepwater Horizon oil spill, also in the Gulf, in 2010. Aware that OPEC’s control over the oil price may diminish, and that longer-term pressures on oil come from climate change and “peak demand”, BP is aiming to ensure that three-quarters of such cost-savings are structural, and that only a quarter of them are subject to cyclical upswings.

There is scepticism about the industry’s ability to keep its belt tight. Share prices of oil-service companies, including offshore-focused ones like Schlumberger, have jumped since the OPEC deal, suggesting investors expect them to be able to raise the prices they charge their paymasters.

BP executives discuss several ways of keeping costs under control, though they admit they are only “scratching the surface” on these. The firm has pulled out of potentially expensive greenfield projects, such as the Great Australian Bight, and opted for better-known territories instead. (Shell, meanwhile, has given up on the Arctic.) BP may not add to its 45bn barrel stock of resources, which at current rates of production could last 52 years. It may replace uneconomic barrels with cheaper ones, but will also draw 15 billion of them by 2030.

Executives have been scouring other industries—from Silicon Valley to carmakers—for examples of how to become leaner. That will involve streamlining inventories and manpower. For instance, in parts of America, BP has cut the number of people monitoring wells by three-quarters, using mobile apps instead. It plans to run fibre optics down its wells to “listen to” problems, such as the seepage of sand, far below the surface, thereby forestalling the need for expensive work.

Andrew Latham of Wood Mackenzie, a consultancy, says that as well as cost-cutting, Big Oil’s best bet on a more economically-sustainable future is gas, which can be cheaper to produce and easier to find than oil. There may be still plenty more gas elephants to bag. They won’t, however, have quite the cachet of the oily ones.