A vigorous debate has broken out among senators, and House leaders, about how President Donald Trump’s impeachment trial ought to be conducted. In an opening salvo, Senate Minority Leader Chuck Schumer, D-N.Y., sent Senate Majority Leader Mitch McConnell, R-Ky., a letter outlining the procedures he believes the Senate should employ — asserting that subpoenas should be issued to four senior administration officials whom Trump prohibited from testifying in the House’s impeachment inquiry (notably, former national security adviser John Bolton and acting White House chief of staff Mick Mulvaney).

McConnell replied on the Senate floor that Schumer “misunderstand[s] constitutional roles” and flatly rejected his proposals. Then, in an opinion article in the New York Times, Sen. Kamala Harris, D-Calif., accused McConnell of laying the groundwork for “a Senate coverup.” Now, House Speaker Nancy Pelosi, D-Calif., says she may hold off on sending the articles of impeachment until she’s confident the Senate will hold a fair trial.

This debate is remarkable because McConnell is unlikely to be making the key decisions about the shape of a Senate trial. The contours of the trial will be set by rules dating to the impeachment of President Andrew Johnson, in 1868. Those rules leave answers to such questions as whether witnesses will appear, and when the trial may be adjourned, to the chief justice of the United States, John Roberts, who — as set forward in the Constitution — presides over the proceedings. By comparison, Schumer and McConnell are bit players.

To be sure, senators can pass a special resolution setting rules for Trump’s trial, as they did for President Bill Clinton’s; such a resolution is the subject of last week’s skirmishing. But doing so would require more comity than is evident, as it needs a supermajority of 60 votes and there are just 53 Republican senators. Absent a special resolution, on the questions now causing debate, senators must defer to Roberts — or overrule him, if they dare.

McConnell could propose, in advance, a partisan resolution setting rules Democrats dislike, but then Democrats could filibuster. McConnell could try to do away with the filibuster, but that would require the support of almost his entire caucus, including vulnerable senators he needs to protect, who represent states that are increasingly voting Democratic — such as Susan Collins of Maine, Cory Gardner of Colorado, Thom Tillis of North Carolina, and Martha McSally of Arizona. It also would probably doom the filibuster for ordinary legislation, which McConnell wants to keep.

Assuming there’s no special resolution, once the House presents articles of impeachment to the Senate, the Senate’s standing rules make the chief justice responsible for both trial preparations and the trial itself; all motions would be directed to him. The motions could come either from the representatives the House appoints to manage its impeachment case or from the president’s defense lawyers.

To make clear their disdain for the entire process, the president’s lawyers could move for dismissal of the articles before the managers for the House even begin presenting evidence. Early motions to dismiss are allowed in criminal trials where the indictment or information fails to allege an actual crime. But unless Roberts believes the conduct described in the articles of impeachment would not constitute lawful grounds for removal of a president even if proven, he probably would deny such a motion. Whether or not one thinks Trump actually abused his office or obstructed Congress, surely the chief justice would not be prepared to say that no president could ever be impeached and removed for such acts.

The House’s impeachment managers, in turn, could move for the issuance of subpoenas to the current and former administration officials who refused to testify in the House on the president’s orders. Again, it’s difficult to see what basis Roberts would have for refusing to issue such subpoenas. The power to compel unwilling witnesses’ testimony is fundamental to the prosecutorial function, which the House assumes in an impeachment proceeding. (If witnesses still defied the subpoenas, the issue would go to court, probably in an expedited process.)

On either a motion to dismiss from the president’s lawyers or a motion to subpoena witnesses from the House, the chief justice could, it is true, decline to rule and put the question to the full Senate. But declining to rule on such simple questions in favor of McConnell — who has declared his intent to shield the president — would widely be perceived as a hyperpartisan move and would call the integrity of all his decisions into question. Given Roberts’s repeated efforts to preserve the public’s esteem for the Supreme Court as a body above politics, he seems unlikely to take such a step.

Once Roberts ruled on a given matter, any senator could seek a vote of the Senate to overrule him. This would require only a simple majority. Republicans have such a majority — so long as they lose no more than two of their senators. However, voting to overrule Roberts — a staunch conservative appointed by a Republican president and confirmed by a Republican Senate — to short-circuit a full airing of the charges against the president might well make some senators uncomfortable. Between those senators who have announced their retirement — Lamar Alexander of Tennessee, Mike Enzi of Wyoming, and Pat Roberts of Kansas — and those facing difficult re-election battles (again, Collins, Gardner, Tillis and McSally), McConnell probably could not count on limiting defections to two.

Once the House rests its case, Trump’s lawyers would have to decide whether to mount a defense or to move for dismissal. Again, the decision about dismissal would not belong to McConnell. Granting a motion to dismiss at the conclusion of the House’s presentation of the evidence would be the equivalent of the Senate voting to decide the case in Trump’s favor, and the chief justice probably would allow it to go to the full Senate. Unless more than two Republican senators wanted to prolong the proceedings, the case presumably would end there.

In short, Democrats who complain that McConnell has not committed in advance to acceptable trial procedures fundamentally misconstrue his limited authority. And Pelosi’s withholding of the articles is nonsensical: It’s a bit like the electric company threatening not to send you a bill until you get rid of your television. As McConnell has pointed out, the House gains no leverage by “refraining from sending us something we do not want.” He would welcome the chance to avoid making vulnerable Republicans choose between alienating Trump’s supporters and offending moderates troubled by the president’s actions. The threat of not triggering such a trial — which makes the process look even more tactically political — is more likely to make him dance a jig than to offer any concessions.

McConnell has no reason to agree to special rules giving Democrats more than the Senate’s standing rules already provide. But those standing rules probably would provide for a reasonable airing of the charges against the president. They would force senators to vote in response to a full, public record. McConnell will no doubt be a determined and effective advocate for the president, but he simply lacks the power to turn the proceedings into the farce Democrats fear.

David Super is a professor of law at Georgetown University. He wrote this article for the Washington Post.