Yet another company has filed for bankruptcy, as the energy industry and its lenders brace for a prolonged slump.

Paragon Offshore, which operates rigs from the Gulf of Mexico to the North Sea, filed for Chapter 11 bankruptcy protection Sunday evening, the latest filing in a painful shakeout buffeting the oil industry.

Over the last 16 months, about 60 oil and gas companies have filed for bankruptcy as commodity prices slide, and that figure is expected to double in the coming months if prices remain low. All told, analysts say as much as a third of the sprawling oil and gas industry in the United States could be consolidated as a result of the downturn.

Paragon, based in Houston, was one of the more fortunate companies that has contemplated bankruptcy. The company was able to negotiate a deal with its lenders — a mix of bondholders and banks — ahead of its bankruptcy filing.

The so-called prepackaged bankruptcy agreement sealed last week allowed Paragon to cut its $2.7 billion of debt by about $1.1 billion and to keep operating.

, the swift drop in oil prices from $100 a barrel in late 2014 to just around $30 last week has drained cash reserves so quickly they have not been able to agree on an out-of-court debt restructuring, which is likely to lead to a series of drawn-out and messy bankruptcies.

Unlike other recent oil restructurings, which have all but wiped out equity holders, Paragon’s existing equity investors will retain 65 percent of the company.

Paragon, which traces its roots to and now employs about 2,900 people around the world, had not run out of cash when it filed, but company executives determined that it could not hold out forever, said Lee M. Ahlstrom, Paragon’s senior vice president for investor relations, strategy and planning.

Paragon’s biggest customers for its drilling services, including the Mexican oil giant Pemex and Petrobras of Brazil, have been cutting back on new projects as the global supply remains high.

In the shale oil fields of the United States, there are very few wells that are profitable to drill at current prices. With large producers like Saudi Arabia showing no signs of cutting back production and the global economy slowing, oil executives and investors expect the market to remain in turmoil until 2017.

Last week, oil prices rallied, but not nearly enough to convince investors, lenders and companies like Paragon that a recovery was near at hand.

“Even if oil jumps up to $50 tomorrow, I don’t think you will see a resurgence in drilling activity,” Mr. Ahlstrom said.

Paragon was spun out of , a large drilling company, in 2014 — joining a highly fragmented industry that includes thousands of small oil producers and companies that service them.

During the boom, hedge funds, banks and investors showered these many oil and gas companies with debt. Energy companies on average have more than twice as much leverage as companies in the Standard & Poor’s 500-stock index.

Now all that debt is squeezing companies, as lower oil prices deplete cash flow. Many oil companies are still trying to hold out. Some are increasing production just to make interest payments.

But banks are under pressure from regulators to reel in their credit lines as the default risks mount, while bond investors are looking to salvage whatever they can from their debt investments.

Many lenders will end up owning their former borrowers, as they swap their debt for equity stakes in oil companies.

Paragon, which is being advised by the law firm Weil Gotshal & Manges and the investment bank Lazard, has been taking steps to lower its debt load. Last week, it deferred an interest payment, while it was in talks with its lenders. And as part of the prepackaged bankruptcy deal, bondholders that were owed $984 million will receive $384 million in cash and a 35 percent equity stake in Paragon — which could gain in value when the market recovers.

The hope among oil executives like Mr. Ahlstrom is that production has been curtailed so sharply during the slump that drilling activity will increase quickly again when the oversupply of oil burns off. “Things could come a-roaring back,” he said.