Polluting the Gulf of Mexico with millions of barrels of oil was bad enough. BP wants the courts to save money by rewriting the terms of a settlement agreement in the 2010 blowout of the offshore rig Deepwater Horizon. This looks like buyers' remorse from a company that benefited from having thousands of individual claims resolved in a single swoop. An appellate court Friday correctly held BP to the settlement it signed. The company and the courts should now turn their attention to ensuring an orderly flow to the claims process.In court filings and national newspaper advertisements, BP has faulted the administration of the Gulf settlement program — the fund established in 2012 to pay for economic losses from the spill. It alleged fraud, corruption and questionable payments. U.S. District Court Judge Carl Barbier, who is overseeing the case, denied BP's request last month that claimants be forced to prove any damages were caused directly by the spill. Barbier noted that the settlement included a waiver for claimants in zones nearer to the spill, creating an assumption that the claims were valid. This blanket language was the price BP accepted to resolve these claims in a timely manner and to avoid thousands of individual lawsuits.The court-appointed fund administrator has an obligation to process the claims responsibly and root out any fraud. But at more than 1,000 pages, the settlement is hardly a half-baked framework for determining the legitimacy of monetary losses. BP has legal avenues to ensure the fund administrator and the trial courts disburse the money appropriately. It also has a legal duty to stand by the agreement.The settlement, after all, gave BP some certainty about the extent of its liability for the spill in exchange for getting money into the hands of its victims as quickly as possible. That trade-off is a straightforward principle of contract law. It shouldn't be torpedoed by a public relations campaign aimed at undoing an agreement one side suddenly finds unacceptable.BP initially projected the settlement would cost $7.8 billion; in October, it boosted that figure to $9.2 billion. That cannot be a consideration for the courts. The only issue that matters is BP's legal obligation in the settlement agreement, which also had a goal getting reparations to victims without undue delay. The spill to many whose lives and businesses were harmed is not a fading memory. The courts are right to enforce the agreement and hold both the company and the claims program accountable for delivering on the promises made in the aftermath of the nation's worst environmental disaster.