By Dominic Casciani
BBC News home affairs reporter
What is happening this week?
Peers are to vote on Monday on whether to extend the time a suspect could be held without charge from 28 days to 42 days - six weeks.
How have the plans progressed so far?
The House of Commons passed the proposal by a majority of nine in June. Thirty-six Labour MPs joined with opposition parties in rejecting this element of the 92-clause Counter-Terrorism Bill. Conservative and Liberal Democrat MPs claimed the Democratic Unionist Party had been offered inducements - including extra financial help for Northern Ireland - to guarantee its support.
How has the law on detention already changed?
The amount of time that a terrorism suspect can be held without charge has altered significantly in the last eight years.
An overhaul of counter-terrorism laws in 2000 introduced the basic 48-hour detention, extendable to seven days with the permission of the courts.
In 2003 that was doubled to 14 days - and the Terrorism Act 2006 took it to 28 days. That four-week limit came after then Prime Minister Tony Blair was defeated in a bid to introduce 90 days. Gordon Brown initially floated the idea of 56 days after coming to office in 2007 - and later settled on 42 days.
So why does the government want to extend the limit again?
The prime minister and Home Secretary Jacqui Smith say there may be occasions when the police need a lot longer to hold a terrorism suspect before they could bring a charge for a specific crime because of the "scale and complexity" of a threat.
Many investigations which have come before the courts have involved detailed computer evidence which, according to the police, is increasingly found in encrypted forms requiring huge effort to decode.
What are the arguments against the extension?
Opponents say there is no need because powers already exist to extend detention for up to 30 days under emergency powers - dealing with grave threats such as war.
Critics, such as civil rights group Liberty, sat there is no evidence police really need the power and oversight would be insufficient.
There is also the issue of symbolism. A delegation of Muslim leaders has told ministers that the move would have a huge impact within communities which already fear they are in the spotlight.
How has the government sought to win over opponents?
Ministers have proposed a series of safeguards which they say guarantee proper checks and balanced against arbitrary treatment.
Firstly, the home secretary needs to be satisfied there is a "grave exceptional terrorist threat". Secondly, top prosecutors and police must issue a report setting out why they need the power.
Once the home secretary signs the order, she must inform Parliament within two days and both houses must approve the move.
The special powers for 42-day detention are only available to the home secretary for 30 days, after which she must reapply for the powers.
Even while she has these powers, each suspect will be able to challenge any application to hold them beyond 28 days in front of a judge.
Are there any alternatives?
Some opponents say the government is presenting this debate as "all-or-nothing" when there could be other alternatives.
The changes being proposed involve the powers to question someone after they have been charged. But there are calls for this power to be extended yet further to allow police to charge someone earlier, then interview them as more evidence comes to light.
Others argue more secret intelligence could solve the problem - such as showing juries phone taps and other internet intercepts. But police chiefs say there is a world of difference between intelligence material and hard criminal evidence that secures a conviction beyond reasonable doubt.
Another more controversial proposal is to allow terror suspects to be charged on a lower evidence threshold. That charge would then be argued in the court, with the Crown saying it can build its case more fully in the weeks to come.