The impeachment trial of President Donald Trump goes into its second week in the U.S. Senate. Certainly the wish that it would all be over is a rational impulse: Just a few days into the process, the marathon has been wearying for senators, and even the watching public, to endure.

There very well could be a push to end the whole process as soon as possible this week. A summary dismissal might not have the support to pass, but a motion to block further witnesses and documents very well could get the 51 votes it needs.

As much as it seems a long shot, given the political climate, the right thing to do would be to keep the trial open for additional evidence. Hawaii’s two Democratic Senate “jurors” in this trial, Mazie Hirono and Brian Schatz, are firmly on the record supporting additional witness and documentary evidence, but they are in the minority in the upper chamber, so it’s not their call.

There are numerous gaps in the information the U.S. House was able to secure in its inquiry for impeachment. Most could be filled by documents the Trump administration possessed but refused to release after a House subpoena, or by key staffers who were subpoenaed but barred by the president from appearing.

The House has been faulted for not challenging this in court; in fact, the evidence the Democratic majority secured through its impeachment inquiry was incomplete.

But majority leaders also were correct that a court challenge likely would bog down for months, even years: Based on past practice, they said, the president likely would invoke “executive privilege” to withhold evidence.

Trump had asserted the privilege when Congress sought documents on the census citizenship issue, when the full Russia investigation report was being requested, and when White House counsel Don McGahn was asked to turn over documents to Congress.

Letting that essentially stymie the entire process, as House manager Rep. Adam Schiff said, effectively would have nullified the entire impeachment clause of the U.S. Constitution that gives the House the sole authority to bring charges against a sitting president.

And “abuse of power” and “obstruction of Congress” are serious charges, even if they aren’t in the criminal code. Summing up the Ukrainian scandal: Getting around the established institutions of governance, using government resources for strictly personal political gain, improperly appropriates presidential power for purposes other than the public good.

The nearly $400 million in military aid appropriated by Congress, in a bill the president signed, was intended for Ukrainian defense against Russian aggressors. Withholding that for a significant length of time — some of it still hasn’t found its way to Ukraine — imperils a U.S. ally and compromises national security interests.

And that is not within the president’s legitimate power to do, especially given that the purpose — damaging a rival to re-election with an announced “investigation” — was so plainly geared not for a fight against corruption, as Trump claimed, but for himself.

The imperative for pursuing impeachment was about a president pursuing his personal benefit, ignoring the guard rails that separate public service from political pursuits.

FURTHER, in the interim between the House’s Dec. 18 vote to impeach and the Senate trial, new complications have surfaced. One was the finding by the nonpartisan Government Accountability Act that Trump’s hold on the military aid to Ukraine violated the law.

Another is a report from Lev Parnas — an associate of the president’s private attorney, Rudy Giuliani — implicating the administration more broadly in the scandal. Parnas’ federal indictment on campaign finance charges certainly tarnishes his credibility, but there is corroboration in some documents he’s released.

And now the Senate is in a uniquely strong position to get more evidence — despite the fact that the president has threatened to invoke executive privilege to shield subpoenaed documents or testimony from the trial.

Some in the GOP leadership point to this as a reason to avoid a long legal battle by rejecting calls for evidence. These calls are bound to come Friday, once the White House completes its defense arguments and after a period for questions.

But others counter that the Senate is in a unique position to insist on more evidence. In U.S. v. Nixon, the high court found that executive privilege must be balanced against the congressional powers of oversight. Some scholars say the judicial branch is unlikely to interfere and that the Senate would have the final say.

It is worth the effort, in any case, to get as full a picture as possible — even if the Senate eventually votes to acquit, as it’s likely to do.

Critics of the impeachment process say the voters should decide how to weigh Trump’s future in the coming election. If that’s so, the Senate should equip them to make as informed a vote as possible.