Speaking to reporters after the hearing, one of Mr. Guzmán’s lawyers, William B. Purpura, speculated that the marshals would house Mr. Guzmán at — or near — the Brooklyn courthouse during trial days, but, he said, he wasn’t sure if his client would return to Manhattan for the weekends.

“They’ve done it before for other proceedings,” Mr. Purpura added, “where they’ll build a facility here.”

All of this fretting is necessary because Mr. Guzmán, 61, has twice escaped from maximum-security prisons in Mexico — once, according to his lore, secreted in a laundry cart and once by way of a mile-long tunnel that was dug into the shower of his cell.

When Mr. Guzmán was extradited to New York last year to face charges of running a vast and violent criminal empire, federal officials promised there would be no tunnels this time. They placed him in what is called 10 South, the most secure wing of the city’s most secure federal jail, the Metropolitan Correctional Center. There, Mr. Guzmán is locked behind bars for 23 hours a day and is denied most visitors except for members of his legal team. His lawyers have argued that the harsh conditions of confinement have hindered his ability to prepare for trial.

The most sobering accusation the government has made so far in the case is that Mr. Guzmán personally ordered the deaths of thousands of people during his decades-long reign atop the Sinaloa drug cartel. In recent months, federal prosecutors have started to reveal the names — and the manners of death — of some of his alleged victims, including members of Los Zetas, a rival drug cartel, whom he is said to have shot in the head after relaxing over lunch. But many of those who were killed years ago have been identified only by their categorical labels: “Informants,” for example, or “members of law enforcement.”

At Tuesday’s hearing, Judge Cogan said he was inclined to exclude from the trial at least some of the evidence about these vaguely described assassinations, which would severely limit the number of murders that the jury in the case may ultimately hear about. Judge Cogan added that he planned to publish an order on the issue of the killings later this week.

Mr. Guzmán’s other lawyer, A. Eduardo Balarezo, has complained about the lack of details concerning these killings, saying it is almost impossible to defend his client when all the government has revealed to him is — to give just one example — that Mr. Guzmán killed an untold number of unnamed “associates who betrayed” the drug cartel at some point between 1989 and 2014.

“We are defending this case with two hands tied and one eye closed,” Mr. Balarezo said.