BP shares rose 2% in heavy trading Wednesday. The modest rebound came a day after shares of the oil producer went into free fall, as efforts to cap a gulf oil leak failed and the government promised a criminal investigation of the biggest-ever U.S. oil spill.

But with BP facing mounting cleanup costs and its legal and political problems seemingly growing, it’s too early to sound the all clear on the stock. The price buying credit default insurance on BP debt soared to an all-time record for the second straight day, as investors sift for clues about the company’s financial future.

The cost of insuring against default on BP jumped 53% Wednesday, reaching $258,000 annually for five years of protection on $10 million worth of debt. That’s up from $179,000 yesterday and $100,000 last week.

Similar rises were taking place at Transocean , up 67% from yesterday at $218,000, Pride , up 34% at $470,000, and Anadarko , up 43% at $474,000. All except Transocean saw their shares rise 2% or so. Transocean, meanwhile, dropped 4%.

The fear seems to be that the oil sector’s problems are as intractable as the Gulf oil leak itself. For instance, it is now more expensive to insure against a default by BP, whose annual pretax profits have ranged between $26 billion and $36 billion over the past five years, than on one by Morgan Stanley , which recently ran a string of quarterly losses and was saved only two years ago by the government.

Given the oil company’s mishandling of the leak and its lackluster management of the cleanup, it seems safe to say a federal bailout isn’t a good bet right now.