The Lords may vote on whether to scrap former justice secretary Ken Clarke's plans altogether- but the Labour party have implied that now that the safeguards have been agreed they will not attempt to derail the legislation.
Lord Pannick, an independent peer, said:
CMPs are a radical departure from common law principles, which we would all respect and approve, that a party to a case has the right to see the evidence against him and has a chance to answer it.
This is a departure from the principle of transparent justice.
The second reason we should be very careful is that a CMP is inherently damaging to the integrity of the judicial process.
Judicial decisions are respected precisely because all the evidence is heard in open court subject to acceptance and judges give a reasoned judgment which explains their decision.
The Government has so far been defeated three times in the House of Lords this evening - and may well be defeated on several more votes.
Peers are voting on amendments to the controversial secret court legislation. The Justice and Security Bill allows more cases to be held in secret without claimants being able to hear the evidence against them.