A U.S. district judge in New Orleans has accepted a $4 billion criminal guilty plea by BP plc over its role in the catastrophic 2010 oil spill that fouled the Gulf of Mexico. But BP’s lawyers still have plenty of work to do managing the company’s massive liabilities over the disaster.

In November BP entered guilty pleas for felony counts of obstruction of Congress and for “seaman’s manslaughter” for the death of 11 workers, and also pleaded guilty to two misdemeanor counts of negligent conduct under the Clean Water Act and the Migratory Bird Treaty Act. On Tuesday Judge Sarah S. Vance approved the agreements, which include $4 billion in penalties and fines. Under the terms of the deal, BP will pay a record $1.26 billion criminal fine and submit to monitoring of its future drilling operations.

As we previously reported, a Kirkland & Ellis team led by partner Mark Filip worked closely on the criminal plea deal with F. Joseph Warin of Gibson, Dunn & Crutcher, who represents BP’s board. The agreement leaves pending criminal charges against two BP well-site leaders accused of involuntary manslaughter, seaman’s manslaughter, and Clean Water Act violations. Former BP executive David Rainey also continues to face charges of withholding information from Congress about the amount of oil that spewed into the Gulf.

According to a statement from BP, at Tuesday’s hearing before Judge Vance BP vice president Luke Keller said the company was “deeply sorry for the tragic loss of the 11 men who died and the others who were injured” in the Deepwater Horizon explosion in April 2010. “Our guilty plea makes clear, BP understands and acknowledges its role in that tragedy, and we apologize–BP apologizes–to all those injured and especially to the families of the lost loved ones. BP is also sorry for the harm to the environment that resulted from the spill, and we apologize to the individuals and communities who were injured.”

Tuesday’s $4 billion deal comes on top of BP’s estimated $7.8 million agreement with plaintiffs who suffered economic loss and injuries related to the spill. New Orleans U.S. District Judge Carl Barbier, who’s overseeing federal mulitdistrict litigation over the spill, granted final approval to the civil settlements in orders issued in December and January. Stephen Herman of Herman Herman Katz & Cotlar and James Roy of Domengeaux Wright Roy & Edwards are co-liaison counsel for the plaintiffs in the New Orleans MDL. BP has relied on a defense line-up that includes Arnold & Porter, Covington & Burling, Kirkland & Ellis, Liskow & Lewis, and SNR Denton.

Meanwhile, BP and its erstwhile drilling partners in the Gulf are still facing close to $20 billion in potential civil fines for alleged Clean Water Act violations in litigation brought by the federal government and Gulf states. (Penalties under the Act can range from $1,100 to $4,300 per barrel of oil discharged.)  BP’s lead lawyers in the remaining litigation, who include Kirkland partners J. Andrew Langan and Timothy Duffy as well as Robert “Mike” Brock of Covington & Burling, filed papers with Judge Barbier earlier this week asking that only BP’s allocution from the guilty plea come into evidence in further proceedings, not documents or statements made by prosecutors during the criminal proceedings. The judge is set to hold a bench trial starting Feb. 25 to apportion civil liability between BP and other companies involved in the spill, including Transocean and Halliburton.

One relative bright spot for BP in the wake of the Deepwater Horizon disaster has been its success in fending off shareholder claims. Last February U.S. District Judge Keith Ellison in Houston gutted a securities class action claiming that BP duped investors about the risks of its operations, and earlier this month the company’s lawyers at Sullivan & Cromwell won a ruling from the U.S. Court of Appeals for the Fifth Circuit upholding a lower court’s finding that related derivative claims should be heard in the U.K., not the U.S.