No other place has had problems on the scale of Jefferson County, the most populous county in Alabama. It has been sinking under a $3 billion debt burden for several years, and the hundreds of millions of dollars in fees it owed J. P. Morgan on the derivatives compounded the problem. The county has made drastic cuts in services and has warned for months that it might have to declare bankruptcy.

Image Larry Langford, a former public official, was convicted in the case. Credit... Dusty Compton/Tuscaloosa News

The S.E.C. did not point to anything improper about Jefferson County’s bonds, its derivatives, or with the once-popular concept of linking the two. Its complaint focused solely on what it called unlawful activity in J. P. Morgan’s efforts to win the business.

It said the two former bank employees, Charles LeCroy and Douglas MacFaddin, had arranged for illegal payments of more than $8 million to friends of the county commissioners, who then worked to make sure the commissioners voted to give J. P. Morgan contracts to underwrite the county’s bonds and provide the derivatives, known as interest-rate swaps.

A lawyer for Mr. LeCroy, Lisa Mathewson, said the S.E.C. had overstepped its jurisdiction and labeled permissible business practices as fraudulent.

A lawyer for Mr. MacFaddin, Richard F. Lawler, said his client denied violating any securities laws and believed he would be vindicated at trial.

The former County Commission president, Larry Langford, was convicted last week of accepting luxury gifts and cash totaling $235,000 in connection with the scheme. He was serving as mayor of Birmingham, Ala., Jefferson County’s largest city, but was automatically removed when he was convicted. The two former bank employees did not settle with the S.E.C. The suit said that J. P. Morgan passed the cost of the illegal payments to the county by charging above-market prices on the interest-rate swaps.

J. P. Morgan did not admit or deny any of the government’s accusations. It said in a statement that it had discontinued its business of trading in derivatives with states and local governments. It also pointed out that the settlement did not impair any of Jefferson County’s bonds.