Rep. Mike Conaway, R-Texas speaks on Capitol Hill in Washington. Conaway has been tapped to lead the House probe into Russian interference in the 2016 presidential election. (Carolyn Kaster/AP)

After a rocky start, the House Intelligence Committee is plowing full steam ahead on its Russia probe with new leadership, a new witness list and new plans for hearings.

Republicans and Democrats on the committee have agreed on a witness list that is dozens of names long and includes campaign and transition team surrogates of President Trump who volunteered to be interviewed, according to two panel Democrats. The volunteers who have come forward include former Trump campaign manager Paul Manafort, former campaign advisers Carter Page and Roger Stone, and former national security adviser Michael Flynn.

Members have also overcome bitter discord that threatened to undermine the committee probe under the tenure of Rep. Devin Nunes (R-Calif.), who after being accused of coordinating with the White House handed over leadership of the investigation to Rep. K. Michael Conaway (R-Texas) earlier this month. Democrats on the committee are singing the praises of the conservative Conaway as “very fair-minded” and “very cooperative,” with one — Rep. Mike Quigley (D-Ill.) — even noting he had “nothing negative at all” to say about him.

But the bipartisan zeal is hitting a few snags with their Senate colleagues. Lawmakers are trying to iron out who will get first crack at key witnesses, such as former director of national intelligence James R. Clapper and former acting attorney general Sally Yates.

A Senate Judiciary subcommittee controlled by Lindsey O. Graham (R-S.C.) scheduled both Yates and Clapper to publicly testify on May 8. That leaves House lawmakers to scramble so they don’t miss their chance to have maximum impact grilling them in open session in the future, or run into problems trying to schedule them for a second trip to Capitol Hill.

“We’re going to want to get through our entire witness list independent of what the Senate may do,” Rep. Jim Himes (D-Conn.), a senior Intelligence Democrat said Wednesday, adding: “The Judiciary Committee over there obviously has questionable jurisdiction over people like Clapper and [former CIA Director] John Brennan.”

Himes said that House Intelligence was going “back and forth” with Graham’s office about “how can we do this in the most efficient manner possible” — perhaps by holding a joint hearing, or splitting up the witness list. House Intelligence invited Yates, Clapper and Brennan to testify publicly after May 2, when FBI Director James B. Comey and NSA Director Adm. Mike Rogers are scheduled to give the panel a closed-door briefing.

But Graham said Wednesday that any such negotiations were “news to me” and that his committee’s process is “moving forward.” As for the jurisdictional concern, he noted that he had received a go-ahead from Senate Intelligence Committee Chair Richard Burr (R-N.C.) to invite Clapper, which was permission enough.

Having Yates, Clapper and Brennan speak publicly to House Intelligence is symbolically important to establishing Conaway as in charge after Nunes, whose tenure continued to sour when he canceled a public hearing at which the trio was scheduled to testify. Reinviting them was one the first moves Conaway made.

Conaway, who was once on the shortlist to become House Intelligence chairman instead of Nunes, has built a reputation as the GOP’s cleanup guy when the party needs to put its house in order.

A decade ago, the House Republicans campaign arm tapped Conaway, a certified public accountant, to uncover an embezzlement scandal involving the organization’s treasurer.

“Mike did what Mike does: He takes care of problems,” said Rep. Tom Cole (R-Okla.), who was the organization’s chairman at the time.

He said Conaway would follow the same playbook with the Russia probe.

“It will be professional, it will be transparent, everybody will have open input, and at the end of the day if there’s anything there, we’ll know what it was and he’ll be completely forthright and honest with whatever he finds,” Cole said.

In 2013, Conaway became chairman of the House Ethics Committee, where his then-ranking Democrat Linda T. Sánchez (D-Calif.) also had a positive experience.

“I always felt like I could trust him, that his purpose was to get through the work, and to do it thoroughly, well, and try to do it dispassionately,” she said. “I hope he brings that same perspective to run an investigation with respect to Russia.”

Conaway himself is staying tight-lipped about the investigation, and promising “to do most all of this together” with ranking Democrat Adam B. Schiff (Calif.)

Praise for the House’s new panel chief comes at the same time that across the Capitol, some Democrats are coming down on the Senate Intelligence Committee for not moving fast enough on its Russia probe.

“I think the Senate committee should move more quickly, it’s gone very slowly,” Senate Minority Leader Charles E. Schumer (D-N.Y.) said this week.

Even Burr has expressed an interest in picking up the pace, after completing an opening round of over 20 interviews with intelligence analysts. He promised that by next week, the number of staffers working on the Russia probe will increase from seven to nine.

On Wednesday, the law firm Saul Ewing announced that one of those new investigators will be April Doss, the former associate general counsel for intelligence law for the NSA.

“The unfortunate thing is we do a majority of our work behind closed doors, versus the public process that seems to go on the other side of the Hill,” Burr said Tuesday. “But we’re satisfied with our progress.”