Image caption BP was fined $87m (£53m) for failing to correct safety hazards at a Texas refinery after a 2005 explosion

Big business lives by different rules to the rest of us.

We are told that when we're in a hole, we should stop digging.

When big business is in a hole, it calls in the advertising department and the image consultants to strategise.

Their job is to persuade the public that the hole is a three-dimensional, subterranean creative resource and the shovel you were using to dig it is a spatial re-alignment adjustment device.

The problem isn't solved exactly but it is re-defined - if you get it right, the company sheds the baggage of an awkward past and heads towards its next set of quarterly results with a whole new image.

BP so nearly got it right.

In the wake of an explosion at its refinery in Texas City, Texas, a few years back, the company found itself facing two charges which threatened its image in the United States - that it was careless with the safety of its workers and reckless about the environmental impact of its core business.

The result was an advertising campaign designed to imply that BP was barely an oil company at all - more a kind of New Age purveyor of clean, green energy.

In one particularly trippy TV ad, a carload of cartoon toddlers grooves its way past the gloomy, threatening gas pumps of rival oil companies before choosing the broad, sunlit uplands of a BP station.

'Beyond Petroleum'

BP didn't stand for British Petroleum any more. The name meant Beyond Petroleum. Here was a company that would give us the energy we craved by communing with winds and waves around the world.

The disaster on the Deepwater Horizon drilling rig, though, has called for something less glib and more convincing by way of response from the company. BP's advertising dollar these days is going on a series of spots in which American-accented company employees deliver straight-to-camera pledges to plug the leak, clean the Gulf and pay the bills.

Image caption Mr Hayward is set to stand down after sustained criticism of his handling of the Gulf of Mexico oil leak

Chief executive Tony Hayward - whose desire to "get his life back" enraged Americans and whose slightly Pooterish English accent probably grates with them - is nowhere to be seen.

His last really high-profile involvement in the battle to restore BP's reputation came when he appeared before a Congressional Committee on Capitol Hill to face the wrath of America's legislators.

His dogged stonewalling infuriated them but attitudes towards BP in the United States - even on the Hill - are more complex than you might imagine.

There's anger of course, but there's also a recognition that the company has to remain viable in the longer term.

That's not just because it has to be able to pay compensation for fouling the Gulf of Mexico - it's also because BP is such a significant player in the American energy market.

Before I travelled to Texas City, Texas - a humming, hissing network of refineries where memories of the BP explosion are still painfully raw - I spent a little time on the Hill talking to two Texan representatives, Democrat Sheila Lee Jackson and John Culberson, a Republican.

Image caption The explosion at the BP refinery in 2005 left 15 people dead

I've no doubt that on some issues they are separated by a gulf as wide as the one that BP has fouled off the southern coast of the United States, and there are differences in their attitudes toward BP too. But they both took the view that BP had to remain in business and in profit to fulfil its obligations.

Ms Lee talked of the need for "remedy and respect" but told me that she had not heard any Americans "calling for the demise of BP".

Mr Culberson said his constituents recognised that "oil is a risky business" but added that as voters in a state where Big Oil is a big employer and a big taxpayer too, they also recognised that "this was the first blowout in 50,000 wells drilled in the offshore waters of the United States."

Production before safety?

Part of the charge against BP in the United States is one which tends to wash around in the background of discussions more often than it is put explicitly as a charge. It is the allegation that the company is responsible for more safety violations than other oil companies and has (or had) a culture that put production before safety.

You shouldn't have to risk your life for a job to provide for your family Katherine Rodriguez, Daughter of worker killed in 2005's BP explosion

In Texas City I met Katherine Rodriguez, one of four sisters with every reason to want to see the company brought down.

Their father was killed in an accident at BP's Texas City plant a year before the 2005 explosion in which 15 men died.

Katherine and her family want to see American law changed so that companies who kill their workers through carelessness or bad working practices are punished much more severely. I thought the fine for the accident which killed their father was low at just $102,000 (£66,000) but the average fine for such accidents is only $5,000 ($3,227).

When she heard the news of the Deepwater Horizon disaster, Katherine says she was heartbroken: "Because more families were going to go through what we had already been through - you shouldn't have to risk your life for a job to provide for your family."

Significantly though even Katherine and her family who have reason enough to hate BP want it to stay in business and in profit.

Texas City is an oil town and firms like BP provide secure, well-paying jobs. She still knows people who work there.

Raymond Guidry, who runs a small metal workshop in Texas City, makes the same point.

Half his business making replacement parts for pumps and pipes in refineries comes from BP, and without them he'd be in trouble.

It's all very well for consumers in non-oil states to talk about boycotting BP gasoline, he says, but lots of small businesses rely on BP. So "if they've got problems, we need to help 'em, not beat up on 'em".

But there's one shadow over BP which refuses to lift entirely - Lockerbie.

The Lockerbie bomber

If there's any truth to the charges - which BP denies - that it may have lobbied for the release of the Lockerbie bomber Abdelbaset al-Megrahi as part of a deal to secure Libyan drilling licences, then the resulting scandal would threaten the company's future in the United States.

The Republican Congressman John Culberson, a big friend of big oil, put it like this…." God forbid - I can't believe it would be true but if they helped get this scumbag released, then I just don't see how they would recover from that."

So for the moment, Deepwater Horizon is damaging for BP but survivable if only because, while the company is hard for Americans to live with at the moment, it would be harder still to live without.

But don't forget Lockerbie. BP's executives may feel that the company is over the worst of this but its not entirely out of the deep, oily water just yet.