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By Helen Catt & Joshua Nevett
BBC Politics
The UK government is expected to change the Illegal Migration Bill to limit detention periods for children and pregnant women.
MPs will vote on Tuesday on 20 changes backed by peers in the House of Lords.
While Conservative MPs are expected to reject most changes, ministers are offering concessions to get the bill through Parliament.
The bill is central to Prime Minister Rishi Sunak's pledge to stop small boats crossing the English Channel.
The bill has been brought into sharper focus by the latest figures on crossings, which showed more than 1,000 migrants made the dangerous journey over two days last week.
Mr Sunak's spokesman said the number of crossings was "still too large" and could escalate further over the summer.
The Illegal Migration Bill is the government's attempt to deter people from making the crossing by toughening up the rules and conditions around seeking asylum.
The bill originally removed the existing time limits on how long unaccompanied children and pregnant women could be detained, but they were reinstated by peers in the Lords.
The BBC has been told the government will agree to keep the current limit on detaining pregnant women at 72 hours.
The government is also expected to limit the amount of time for which unaccompanied children can be detained to eight days.
As the bill completed its latest stage in the Lords, Home Office minister Lord Murray told peers ministers were "reflecting on each and every amendment".
Later, he said it was "clear that there will be some changes" to the bill, without specifying what they might be.
The government's efforts to curb the number of small boats crossing the Channel have been hampered in Parliament and the courts.
A plan to house house migrants on a barge moored in Dorset has been delayed.
And the government's policy of sending migrants to Rwanda is set for a legal battle in the Supreme Court.
The bill would place a legal duty on the government to detain and remove migrants arriving in the UK illegally, either to Rwanda or another "safe" third country.
The government has stressed it remains committed to its plan to remove migrants to Rwanda, and has said it will challenge a Court of Appeal ruling last week that this was unlawful.