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Key Republican senators told CNN the Senate should conduct a fulsome trial of President Donald Trump – assuming the House soon sends over articles of impeachment, as expected – and not try to jam through a motion that would allow them to dismiss the case quickly on a partisan vote.

A motion of dismissal was attempted in the 1999 impeachment trial of President Bill Clinton when his Democratic allies in the Senate, led by the powerful institutionalist Sen. Robert Byrd of West Virginia, tried and failed to get that case dismissed. Even though Byrd rounded up some support from Republicans who controlled the chamber, his effort fell short and the trial went on for about three more weeks before Clinton was acquitted.

In the Trump matter, some of the GOP senators who argued against dismissing the case are close allies of the President, who might otherwise be inclined to assist him politically by helping the spectacle go away.

Others have been critical of him at times but are unhappy that the House has conducted its investigation in private, with routine leaks of information damaging to the President, and without due process for him.

They argued a comprehensive and public examination of the charges would be best for Trump, who wants to clear his name and stay in office, best for American people, who deserve to learn what happened, and best for the Senate as an institution, to demonstrate that even in these harshly partisan times, a careful examination of the charges can be conducted.

“Unlike the process up to this point, I think it is important the Senate process be viewed as fair and serious and give serious consideration to whatever the House is going to bring us,” said Sen. John Cornyn of Texas, a member of the Republican leadership, who added that he is “very doubtful that there will be some immediate attempt to try to dismiss the charges.”

Sen. David Perdue, a Republican from Georgia who is close to Trump, said there’s been so much “innuendo and stuff done behind closed-doors” during the House impeachment inquiry that he “personally would welcome an open and fulsome debate.”

“What I want to hear is both sides of the argument. The trial is in the Senate not in the House,” Perdue said in an interview. “But I don’t see this taking weeks and weeks and weeks. This is a very isolated accusation so I would hope we could get a look at it and get it done and give this President due process.”

What McConnell is thinking

Senate Majority Leader Mitch McConnell has not said he wants to force a quick vote to end the case. But he also hasn’t publicly outlined what he thinks an appropriate process should be, outside of acknowledging he is constitutionally required to put it on the floor.

Democrats feared McConnell might try to block a trial – in the way he blocked Judge Merrick Garland’s nomination to the Supreme Court – and were alarmed when the Kentucky Republican began running campaign ads for his reelection vowing to stop impeachment.

“I haven’t heard anyone espousing a quick dismissal,” said Sen. Shelley Moore Capito, a West Virginia Republican. “I certainly think we need to hear it out from the House. This is a serious thing. When you are considering removing somebody from office or impeaching them in that way. I think you’ve got to hear it.”

But there is a temptation by some Republicans – frustrated by what they see as a political exercise in the House aimed at undoing the last election and exhausted by the daily drumbeat of negative news about the President – to use the power of their majority votes to throw out the case as soon as they get it.

“We’ve had this conversation among some of us,” said a GOP senator who asked not to be identified to discuss candid thinking in the Republican caucus. “There’s no decision yet but as you know, under the rules, we think that you could have a motion to dismiss raised at any time in the process, even on the first day, with a 50-vote majority and the Vice President breaking the tie. You could dismiss it.”

Senators of both parties are studying the arcane impeachment rules and looking back on the trials of Clinton and President Andrew Johnson, the only other president to be impeached. They say it’s hard to lay out too specifically a roadmap of what to expect in a Trump trial because much of it will be driven by Chief Justice John Roberts, who will preside over the case and rule on motions.

Before the Clinton trial, Republicans and Democrats – who served in an arguably slightly less partisan time than now – agreed on a set of rules for the proceedings that included allowing Byrd to get a vote on a motion of dismissal two weeks in.

Sen. Kevin Cramer, a Republican from North Dakota, said he doubts the current Senate could agree to a resolution like the one in 1999 and may have to use existing rules.

“The rules as they exist provide the opportunity for either the lawyers for the President or the managers from the House (to be) the only ones who can make that motion – anytime,” Cramer said. “A second layer of rules, that would overlay the original rules, would require some sort of resolution to be passed by the chamber. That would provide the opportunity for senators to make (the motion to dismiss.)”

Either way, Cramer said it would be a mistake to quickly dismiss, both from a political and due process reasons.

“I don’t think it would be wise to dismiss on a 51-49 vote on the first morning or the first afternoon,” he said. “We would owe it at that point to ourselves to at least hear what they are presenting. If within a couple of days, or a few days, it is clear they don’t have impeachable evidence, then perhaps a motion to dismiss would be in order,” he said.

Unclear if the votes to dismiss are there

It’s not immediately clear if Republicans, who hold a 53-47 advantage over the Democrats, could get the votes to dismiss. Some senators, especially those running for reelection next year, may be wary of not giving the evidence a thorough review, but for now most won’t comment.

“Until I see what I see what the House presents to us, I truly can’t make any judgments like that,” said Sen. Susan Collins, a Republican from Maine who is up for reelection in a state that’s trending Democratic. “I just don’t know what various colleagues will decide to do.”

Other senators who have been critical of Trump, also want to hold off deciding if they might support a motion of dismissal.

GOP Sen. Lisa Murkowski of Alaska said it’s “way too early for us to have that discussion.”

Sen. Mitt Romney, a Utah Republican, said: “I think anything related to the impeachment process, I’m going to wait until all the facts come it, before I comment.”

Freshman Republican Sen. Josh Hawley of Missouri said “it is important to follow the Constitutionally-prescribed procedures no matter what they may be.”

“It is my understanding that there is no provision for us that would allow us to say we aren’t going to take this up. We do have to proceed into a trial-like setting,” he said.

“Once we go into that setting, what happens next? How far do we go into it? I think those are all open questions,” he added.

CORRECTION: This story has been updated to correctly identify that senators are studying the impeachment procedures related to President Andrew Johnson.

CNN’s Ellie Kaufman contributed to this report.