How little we know about the Ukraine scheme headlined by Trump’s personal lawyer Rudy Giuliani was underscored by public interviews given last week by Giuliani associate Lev Parnas, who faces a federal indictment in the Southern District of New York.

Parnas made sweeping claims, such as his assertion that Trump was “aware of all of my movements” and that Attorney General William Barr was “basically on the team.” These are provocative and damning assertions. But how does Parnas claim to know all of this?

While there is good reason to be skeptical of these allegations, Parnas provided a trove of notes, texts and other evidence that demand further investigation. For example, Parnas presented evidence that Marie Yovanovitch, then the ambassador to Ukraine, was under surveillance. The American people—and Yovanovitch—deserve to know whether that allegation is true and why Trump’s associates were surveilling our own ambassador. After all, it is possible this scheme constituted a federal crime, such as a conspiracy to threaten or assault a federal official.

This isn’t the only new evidence to come to light since Trump was impeached by the House of Representatives. A few weeks ago, Just Security published unredacted versions of emails that show the internal resistance in the administration to Trump’s scheme to withhold aid as well as an apparent effort to abuse processes established in the Foreign Intelligence Surveillance Act to cover up that resistance.

There are more shoes to drop, given that Bolton has now expressed his willingness to testify—and is writing a tell-all book that could reveal new information that will raise even more questions. Bolton publicly said he would testify before the Senate if subpoenaed, but he previously resisted a House subpoena. Bolton has no principled reason to reject a subpoena from the House given that he is willing to accept one from the Senate.

Right now, Democrats are focused on conducting this investigation via the Senate trial itself. But the Senate trial is not the ideal vehicle to conduct an investigation of this matter, even if Senate Republicans sincerely wanted to get to the bottom of it. In a typical trial, jurors are carefully selected to ensure they don’t know anything about the case or have an interest in the outcome. In the impeachment trial, the “jurors” know a lot about what Trump did and many have a personal stake in the outcome of the trial.

Senators aren’t really jurors either, as then-Chief Justice William Rehnquist noted during the Clinton trial. After all, the jurors in an impeachment trial decide what the rules are, what evidence can be introduced and what witnesses are called. If a jury in a typical case got to set the rules for a trial, trials would rarely last more than a few hours, so jurors could quickly get back to their jobs and families.

In a criminal trial, judges instruct jurors regarding the law and the jury decides questions of fact. The judge decides the defendant’s sentence much later. But in an impeachment trial, the question of whether removal for wrongdoing is warranted—an issue of law and sentencing, in this context—is decided by the senator jurors.