Senator Lamar Alexander of Tennessee had been among a handful of Republicans who were seen as undecided on allowing more witnesses and documents in the trial. But on Thursday he said that while Mr. Trump had acted inappropriately, his dealings with Ukraine were not impeachable offenses.

What’s next: A vote on whether to allow new evidence is expected today. If it fails, Republican leaders could move the trial to final deliberations and a speedy up-or-down vote on each article of impeachment. Here’s what to expect when the proceedings resume at 1 p.m. Eastern.

Catch up: On Thursday, Chief Justice John Roberts, who is presiding over the trial, declined to read aloud a question from Senator Rand Paul that included the name of a person widely thought to be the C.I.A. whistle-blower whose complaint prompted the impeachment inquiry. Here are six takeaways from the question-and-answer session.

News analysis: Alan Dershowitz, one of Mr. Trump’s lawyers, said his arguments that presidents have virtually unfettered power when seeking re-election were mischaracterized. But Mr. Trump himself has promoted an expansive view of executive power that didn’t start with Ukraine, our Washington correspondent writes.