The man waited in a car in the parking lot of a northern New Jersey diner. It was pouring rain and Frank Sinatra’s “Fly Me to the Moon” played on the radio.

Martin Cohen got in the car. Mr. Cohen, a 68-year-old Orthodox Jewish insurance broker from upstate New York, began complaining about a business associate.

Mr. Cohen, now on trial in federal court in Brooklyn in a murder-for-hire case, didn’t realize that the thug next to him was an undercover detective, not a hit-man, and that their September 2002 conversation was being secretly taped.

This week, jurors heard the conversation, which offers a close-up, almost comical look at a murder plot negotiation.

“Don’t do anything drastic,” Mr. Cohen says on the tape. “Maybe give him a signal. Just give him a couple of shots, knocks in the kneecap – something like that. I got a conscience.”

While the tape played, Mr. Cohen, wearing a suit and black yarmulke, sat across the courtroom from the undercover detective, Salvatore Arrigo, an NYPD veteran with a ponytail and a deep, raspy voice.

“Tell me how bad you want him,” Detective Arrigo says at one point. “Legs? Head? What? Do you want him in the hospital for a week, a month?”

“Yeah,” Mr. Cohen says on the tape, “a week would be good.”

The plan was to send a message by roughing-up an associate of the investor Mr. Cohen wanted to scare. The associate, who worked on Madison Avenue in Manhattan, would be beaten as he walked to his Brooklyn home.

“What happens if he gets hit in the head and goes out of the picture – are you okay with that?” Detective Arrigo asks. “Is there any way you can go after a different part of the anatomy?” Mr. Cohen asks.

In the end, they agreed on a $1,000 down payment for the job. Mr. Cohen thanked the detective before exiting the car.

Prosecutors say Mr. Cohen wanted to resolve a long, simmering dispute with the investor. They say Mr. Cohen had millions of dollars in personal, business, and gambling debts.

“One of the ways he was going to lighten his debt load was to hire a hit man,” Assistant U.S. Attorney Monica Ryan said during opening arguments.

A lawyer for Mr. Cohen, Michael Washor, said his client was pressured and manipulated by an FBI informant into participating in the murder plot. His client had wanted to negotiate the dispute, not resort to violence. Mr. Washor said Mr. Cohen “never harmed a fly in his life.”

During opening arguments, the defense lawyer told jurors that Mr. Cohen was taking numerous medications when he met with the detective, including Paxil and Valium.

“You’re hearing the voice of a zombie,” he said. “This man had … five different drugs, at probably the highest degree, being administered to him by his psychiatrist because he could not function.”

Mr. Cohen was tried on the same charge earlier his year, but his trial ended in a hung jury.

His re-trial is expected to end next week. If convicted, Mr. Cohen faces up to five years in prison, defense lawyer Nicholas Pinto said.