As soon as court was back in session on Tuesday, Judge Cogan discussed the secret memo at a second sidebar conference — which was itself conducted in secret. The subject was apparently so sensitive that he immediately placed its transcript under seal.

It was only after the sidebar ended that Judge Cogan gave a vague explanation about what was going on.

Speaking from the bench, he said that he agreed with the prosecutors and would limit the questions that Mr. Guzmán’s lawyers could ask Mr. Zambada on cross-examination. He also said that whatever might be learned from a broader line of inquiry did not outweigh “protecting individuals and entities” who were not directly involved in the case and “who would face embarrassment” if Mr. Zambada were allowed to testify without restraint.

Judge Cogan never identified those “individuals and entities,” and because he sealed the transcript, the government and the defense could not discuss them. Who they were — and why they stood to face embarrassment — remains another secret.

In court on Tuesday, Mr. Zambada did name one of Mexico’s top law enforcement officials, Genaro García Luna, as someone who took bribes. He said that on two occasions he met Mr. García Luna in a restaurant and each time gave him a briefcase stuffed with at least $3 million in cash.

Mexico has long been plagued by troubles with corruption, and some in the country were not at all surprised that tales of graft were emerging, thousands of miles away, at El Chapo’s trial in Brooklyn.

“The world might be shocked, but here, for us, this is old news,” said Fernanda Hernández, 23, a secretary from Mexico City. “To learn the inner workings of corruption at the highest level is something that for some reason feels rather obvious to us.”