"Obviously that it one of the most contentious part of these proceedings," McConnell said about the question of trial witnesses, which will be determined simply by majority vote.
"Fifty one Senators determine what we do," McConnell added in a reminder that there is an inherent risk that a trial could get away from GOP control, if a handful of Republicans were to break ranks, and demand to hear from certain witnesses.
GOP Senators said they had no problems following the outlines of the initial trial rules which were used 21 years ago.
"What's good for President Clinton is good for President Trump," said Sen. John Barrasso (R-WY).
Democrats grumbled about the decision, as they have tried to pressure the GOP to also make an agreement on witnesses for the trial.
"What are the Republicans afraid of?" asked Sen. Debbie Stabenow (D-MI).
Senate Democratic Leader Charles Schumer again tried to make the case that Republicans were ready to hold back information from the public.
At this point, no one knows when the trial will actually begin, waiting to see when House Speaker Nancy Pelosi will send the impeachment papers to the Senate.
"It is a rule of impeachment in the Senate that we must receive the papers," McConnell told reporters, as until then, the trial cannot start.