House Speaker Nancy Pelosi chuckled at the brief mention of a looming question: Which Democrats will she appoint to prosecute the impeachment trial against President Trump in the Senate?

“Right now? Okay, if you promise not to tell anybody,” Pelosi (D-Calif.) told reporters Thursday, breaking into full laughter.

With Democrats confident of having a majority to impeach Trump next week, a new parlor game has broken almost into the open. It’s the next step in the process in which Pelosi has unilateral power to appoint members to serve as impeachment managers in the Senate, presenting their case in what would be only the third impeachment trial of a president.

Many Democrats would like the opportunity to fulfill such a rare, historic role, but they know Pelosi has declared this period “somber” and “prayerful,” cautioning that it would be a task undertaken with “humility.”

In other words, showboats need not apply to be an impeachment manager. If the speaker sees a Democrat openly campaigning for the appointment, trying to boost his or her profile, she will almost certainly knock that candidate off the list.

And, for a leader who has commanded enormous clout within her caucus of late, Pelosi receives utter deference from people who might get the nod.

“I’ll leave that to the speaker,” said House Intelligence Committee Chairman Adam B. Schiff (D-Calif.), walking onto the House floor Thursday afternoon.

“I think that’s a call for the speaker,” said Rep. Jackie Speier (D-Calif.), another Intelligence Committee member, a few minutes later.

Pelosi has no restrictions in choosing whom she sends to the Senate. A decade ago, in the impeachment of a corrupt federal judge, she chose a five-member bipartisan group from the House Judiciary Committee, led by Schiff, who served on that panel until becoming the chairman of the Intelligence Committee.

In December 1998, after approving two articles of impeachment against President Bill Clinton, House GOP leaders appointed 13 Republicans from the Judiciary Committee to lead the prosecution in a trial that ended with the president’s acquittal in early February 1999.

The House approved those appointments in a resolution just after the impeachment votes.

But many Democrats, particularly those in the Senate who will serve as jurors, want Pelosi to send over a mix of lawmakers from the committees that handled the Ukraine investigation, particularly Schiff and members of his Intelligence Committee.

“I think Adam Schiff did a good job, particularly each day summarizing what he thought was presented in evidence,” Sen. Richard J. Durbin (D-Ill.) said Thursday.

Durbin, the No. 2 in Democratic leadership, cited Schiff’s ability to present closing arguments each day of the hearings that his committee held last month with current and former diplomats and national security advisers.

“I hope, if he isn’t leading the team, he’s a co-leader,” Durbin said.

Schiff’s committee eventually prepared a massive report that formed the basis for two articles of impeachment that were set to be approved by the Judiciary Committee late Thursday.

That panel’s chairman, Rep. Jerrold Nadler (D-N.Y.), won the top spot on the committee two years ago in a campaign that touted his constitutional law background and ability to handle impeachment proceedings. He defeated Rep. Zoe Lofgren (D-Calif.), who was also on the committee during the 1998 Clinton impeachment and served as a staffer during the 1974 consideration of Richard M. Nixon’s impeachment.

Despite Pelosi’s tight-lipped approach to the appointments, one thing is certain to be different from the House managers from the Clinton trial — it will be a more diverse group than the 13 white male Republicans who marched to the Senate then.

“Yeah, I don’t think that will happen, I really don’t think that will happen,” Speier said. “I think we’ve got talented people that reflect our ethnic diversity, our racial diversity.”

Two members of the Congressional Black Caucus, Reps. Val Demings (D-Fla.) and Terri A. Sewell (D-Ala.), have played prominent roles in the investigations. Sewell is the third-ranking Democrat on the Intelligence Committee while Demings, a former sheriff, is one of just two Democrats to serve on both the Intelligence and Judiciary committees.

Some Democrats are whispering about a different form of diversity — political and geographic — after the Tuesday news conference announcing the two articles of impeachment. Pelosi was flanked by committee chairmen who had been investigating various allegations against the president, all of whom came from two of the most liberal big cities in America: Los Angeles and New York.

That consideration could boost the chances of Reps. Joaquin Castro (D-Tex.), David N. Cicilline (D-R.I.) and Sean Maloney (D-N.Y.). Castro, chairman of the Congressional Hispanic Caucus, hails from San Antonio and serves on Schiff’s committee, while Cicilline was mayor of Providence.

Cicilline and Maloney are co-chairs of the LGBT Equality Caucus. Maloney would create geographic diversity, representing a rural district north of Manhattan.

He is the only member of the Intelligence and Judiciary committees to represent a district that backed Trump in 2016.

History has a mixed record, at best, for those who prosecute presidential impeachments in the Senate. Sen. Lindsey O. Graham (R-S.C.) and former congressman Asa Hutchinson (R-Ark.) received overall good grades for their arguments in favor of an obstruction charge against Clinton.

Some careers foundered, with a pair losing in GOP primaries in 2002 and several more retiring in the years after impeachment.

Schiff’s career grew out of defeating one of those managers, Republican James Rogan, in an epic House race in 2000 that was then the most expensive in history.

Now a leading contender to be an impeachment manager, Schiff had spent most of this year resisting calls to impeach Trump over the 2016 Russia investigation from his own experience.

“I do know how divisive and consequential the process is. I saw that in 2000,” Schiff said in a July interview.

Now he finds himself at the top of most Democratic lists for potential leaders of the impeachment managers.

Just don’t expect anyone to talk too openly about it.

“When the time is right,” Pelosi said, “you’ll know who the people are.”