US President Donald Trump appeared headed for all-but-certain impeachment acquittal as senators rejected efforts to call more witnesses and moved to start bringing a close to the third impeachment trial in American history.
The timing of a final vote on Mr Trump was still uncertain.
The Senate opened with four hours set for arguments on the question of calling more witnesses.
The outcome was increasingly clear after a key Republican, Lamar Alexander, of Tennessee, announced he didn't need to see or hear more testimony.
He said the Democrats had proved their case, that Mr Trump abused power and obstructed Congress, but he did not think Mr Trump's actions rose to the impeachable level.
As the Senate opened, another GOP senator, Lisa Murkowski, of Alaska, announced she, too, would oppose, saying the proceedings "degraded" the institution.
"I have come to the conclusion that there will be no fair trial in the Senate," she said.
"I don't believe the continuation of this process will change anything. It is sad for me to admit that, as an institution, the Congress has failed."
Separately, 'The New York Times' reported yesterday that a book manuscript by Mr Trump's former national security adviser John Bolton describes a May meeting in which Mr Bolton claims that Mr Trump ordered him to call Ukrainian President Volodymyr Zelensky to encourage him to meet with Rudy Giuliani, the president's private attorney.
Mr Bolton never made the call, he writes in his account, which adds detail to the prosecutors' contention that Mr Trump pressured Mr Zelensky to help with investigations to help Mr Trump politically while Mr Trump was withholding US military aid as leverage.
This was two months before Mr Trump's now-famous phone call with Mr Zelensky which is a focus of the impeachment charges.
Mr Trump denied making the statements.
Eager for acquittal, the president and his allies in the Republican majority resisted efforts by Democrats to keep the proceedings going for weeks.
Voting on the witness question was expected late yesterday after hours of debate, with other votes stretching well into the evening.
Democrats warned the outcome won't mean a true acquittal for Mr Trump but a cover-up.
"They're about to dismiss this with a shrug and a 'who cares'," said the Senate's third-ranking Democrat, Patty Murray, of Washington.
"The full truth will come out."
The impeachment of the president is playing out in an election year before a divided nation.
Primary voting begins on Monday in Iowa and Mr Trump wants action on his trial finished in time for his State of the Union address next Tuesday.
Protesters stood outside the Capitol as senators arrived yesterday, but few visitors have been watching from the Senate galleries.
Despite the Democrats' singular, sometimes-passionate focus on calling witnesses after revelations from Mr Bolton, the numbers are now falling short. It would take four Republicans to break with the 53-seat majority and join with all Democrats to demand more testimony.
Chief Justice John Roberts, in the rare role presiding over the impeachment trial, could break a tie, but that seems unlikely.
Mr Alexander said in a statement there was "no need for more evidence", giving the Trump team the likelihood of a Senate vote in its direction. Not that he accepted Mr Trump's repeated claim of "perfect" dealings with Ukraine.
Mr Alexander told reporters at the Capitol that after "nine long days and hearing 200 video clips of witnesses... I didn't need any more evidence because I thought it was proved that the president did what he was charged with doing.
But that didn't rise to the level of an impeachable offence, so I didn't need any more evidence to make my decision."
Asked whether Mr Trump deserved re-election in the wake of such wrongdoing, Mr Alexander said: "Everyone will have to make that decision for themselves."
Mr Trump was impeached by the House last month on two charges, first that he abused his power like no other president, jeopardising Ukraine and US-Ukraine relations.
The second article of impeachment says Mr Trump then obstructed the House probe in a way that threatened the nation's three-branch system of checks and balances.