Downing Street says it will not force plans for a supreme court through Parliament, after a deal with peers.
Lord Woolf has attacked plans for constitutional change
Commons leader Peter Hain had suggested ministers could use the Parliament Act to push the controversial Bill through the House of Lords.
Peers sent the plans to a special select committee in what ministers saw as an attempt to kill the Bill.
But No 10 is now "happy and content" with the new deal, which includes a time limit for the committee's work.
Peers will vote on Monday on a motion telling the committee to report by 24 June.
They are also set to use new procedures to allow the Bill to continue its passage through Parliament in the next parliamentary session if it is not on the statute books by that time.
The committee will be chaired by former Lords leader Lord Richard and include Lord Chancellor Lord Falconer and his Tory and Liberal Democrat counterparts Lord Kingsland and Lord Goodhart.
Crossbenchers, including former law lord Lord Lloyd of Berwick, will also work on the committee.
Usually, Bills which are not passed in one parliamentary session have to start the whole process again.
Announcing the new deal, the prime minister's official spokesman said talks with Conservative peers had been concluded "satisfactorily".
"We now believe it should be possible that the Bill can be delivered in a sensible way," he added.
Government aides say using Parliament Act was always only an option and no decisions had ever been made.
Mr Hain told MPs on Thursday that the Bill had never gone before MPs on the only previous occasion a committee had been used - in 1975.
He welcomed the new agreement, saying: "Rather than a tactic ... to wreck the Bill, we now have the opportunity for proper scrutiny."
The Tory and crossbench peers who insisted on the extra scrutiny always argued it would still be possible to give MPs time to consider them.