In 2003, prosecutors said, the mayor of a city in Northern Illinois sent a message to the operators of a local strip club: Pay me, or I’ll shut you down.

The mayor of Harvey, Ill., a city of about 18,000 just south of Chicago, knew that the strip club allowed prostitution in a private area of the club, and he demanded $3,000 a month from the business to let it stay open, according to prosecutors.

According to a criminal complaint filed in U.S. District Court in Chicago, the club yielded to the threat, eventually even acquiescing to a demand from the mayor to double its payment to $6,000 per month. The scheme continued for about 15 years, prosecutors said.

On Monday, Rommell Kellogg, 71, the mayor’s brother, was convicted after a weeklong trial of conspiring to demand and collect payments from the club, the office of the U.S. attorney for the Northern District of Illinois said in a statement. Mr. Kellogg could face up to 25 years in prison on that count and up to five years for each of the five counts against him related to conspiracy to commit theft and intimidation, prosecutors said.

Corey Johnson, 68, a cousin of the mayor, pleaded guilty last month to a theft charge for his role collecting money in the scheme, according to prosecutors.

Sentencing dates for the two have not been set.

Gal Pissetzky, a lawyer for Mr. Johnson, said on Thursday that he believed Mr. Johnson’s plea agreement was a “fair resolution.”

Rommell Kellogg’s lawyer declined to comment on Thursday.

The criminal complaint does not name Eric Kellogg, the former mayor of Harvey, and he has not been charged in the case. But federal records show that he was the mayor of Harvey from 2003 to 2019.

Eric Kellogg did not immediately respond to phone messages or emails on Thursday.

It is unclear if federal prosecutors intend to bring additional charges in the scheme. The U.S. attorney’s office declined to comment, noting that sentencing was still pending against the two defendants who were found guilty.

Under the conspiracy, the strip club, whose name is not mentioned in court records, could operate while allowing its dancers to engage in prostitution as long as it paid $3,000 a month to the mayor, according to the criminal complaint. That worked for a few years until around 2007 or 2008, when the mayor wanted the club to double its monthly payment, prosecutors said.

The club’s operators initially refused to pay $6,000 per month, and a police officer arrived at the club days later and ordered the business to shut down, according to a criminal complaint. The club later gave in to the demands for increased payment, and the deal continued even when the owner’s child took over after the strip club’s owner died in 2008, according to the complaint.

The club was searched by federal law enforcement agents in October 2017 based on evidence of tax crimes and prostitution, according to the complaint. The search prompted the club to close for several weeks, and the club’s manager later agreed to work with investigators.

When the club later reopened, the manager was told by investigators not to allow prostitution on the premises, but to continue making payments to the mayor, according to the complaint, which did not name the manager. Investigators documented payments from the club to the mayor from Dec. 8, 2017, to May, 3, 2018, totaling $37,000.

As part of the investigation, the authorities tapped the phones of Mr. Johnson and Rommell Kellogg, and they also obtained some recorded conversations between the club’s manager and Mr. Johnson.

In one conversation between the club manager and Mr. Johnson in December 2017, Mr. Johnson shared a desire to stop working as an intermediary, according to the complaint.

“I never wanted to be in it from the beginning,” Mr. Johnson said during the meeting.

The club manager and Mr. Kellogg had a meeting in January 2018 during which the manager told Mr. Kellogg that Mr. Johnson wanted out of the scheme, according to the complaint.

“Corey told me that he wanted to get out of delivering pizzas,” the manager said, using pizza as their code word for the payments.

Mr. Kellogg said he would not allow Mr. Johnson to stop working as an intermediary, according to the complaint.

“He can’t get out of nothing,” Mr. Kellogg said during the meeting. “He ain’t getting out of nothing because that’s the way it goes. That’s convenient for me, convenient for you. That’s convenient.”

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