Peers have reached a deal to end the deadlock over plans for a referendum on the Westminster voting system.
It comes on the 15th day of debate by peers on the Parliamentary Voting System and Constituencies Bill.
Labour peers have been resisting plans in the bill to cut the number of MPs and redraw constituencies.
Lords leader Lord Strathcylde promised a "package of concessions" and said the bill's committee stage would be completed by Wednesday evening.
The bill has to become law by 16 February to allow a referendum on changing from first-past-the-post to the alternative vote (AV) system to take place on 5 May, as planned.
The deal was reached after crossbench peers' convener Baroness D'Souza called for compromises and put forward an amendment to allow the Boundary Commission to hold public inquiries into proposed boundary changes in some cases.
Peers began debating the amendment, but she withdrew it after the Advocate General, Lord Wallace of Tankerness, told peers: "The government proposes a public hearing process enabling the opportunity for the public and for the parties to express their view."
The Lib Dem minister said this would allow for "sensible discussion" of proposed boundary changes, while still allowing the number of MPs to be reduced from 650 to 600 in time for a 2015 general election.
Lord Strathclyde told peers that agreement had been reached through "the usual channels" - the party whips - on a timetable for completing the bill's committee stage by the end of business on Wednesday.
He added that ministers had held "meaningful discussions" with opposition and other peers, adding: "As a result the government will be bringing forward a package of concessions at report stage of the bill and I'm sure that the whole House will welcome that."
But for Labour, Lord Falconer indicated that further concessions might be necessary if the bill was to get through its remaining report and third-reading stages in time.
He said the agreement to complete this stage of the bill by Wednesday was "the product of good discussions on the content of the bill over the weekend and today".
But he added: "The further timetable depends on further agreement on substantive issues between the parties."
Lord Strathclyde said the bill had to be returned to MPs for debate by Monday 14 February if a referendum was to be held on 5 May.
Peers have been debating the bill's committee stage for 15 days - with one session lasting all night.
Labour peers have resisted the plans to cut MPs and redraw constituencies, while ministers were reportedly considering a "guillotine" motion to end the debate.
Had an agreement not been reached, the guillotine motion would have been used for the first time in the House of Lords' history - the Upper House traditionally regulates its own debates.
Lady D'Souza had criticised the government's original proposal for an outright ban on inquiries as "unreasonable".
Welcoming the government's response, she told peers she had been "encouraged by one or two people to see if there was any way" in which crossbenchers might play a role in ending the stand-off over the bill.
She added: "The other thing that perhaps has moved me, certainly, and a number of other crossbenchers, was the shadow or the threat of anything approaching a 'closure motion' in this House."
The bill proposes holding a referendum on replacing first-past-the-post Westminster elections with the AV system, allowing voters to rank candidates in order of preference - a key Conservative concession to their Lib Dem coalition partners.
The legislation has to go through by 16 February to meet the timetable granted to the Electoral Commission to prepare for a referendum.
The Lords committee stage debate is thought to be the longest since 1971, when peers spent 18 days on the Industrial Relations Bill.
The government has suffered two defeats in the Lords over the planned legislation, and ministers will have to decide whether to risk further delay by asking MPs to overturn them when the bill returns to the Commons.