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.
More top news
Police wanted to question Norman Williams over the suspected murders of his sister-in-law Sheila Jefferson and her husband Dennis Jefferson.
A 93-year-old Second World War veteran has flown over 10,000 miles to be reunited with his wartime sweetheart more than 70 years on.
The Republican presidential candidate is known for making some "interesting" comments - but can you guess who made these?