What is Lord Justice Leveson proposing?
He says a genuinely independent and effective system of self-regulation is needed.
So he's proposing a body that can investigate complaints and fine newspapers up to a million pounds. He wants the Chair and other members of it to be independent.
How to encourage papers to sign up?
There will be an arbitration service and if they don't use it for complaints they could face having to pay big costs, even if they win in court
But what will worry all the papers is that he proposes there is "legislative underpinning". That means that Parliament passes a law to make sure it works and is independent.
The plan is that Ofcom, which regulates broadcasters, will ensure the new press regulator is independent.
And there is a threat that if papers don't sign up the Government could look at something the press really won't like which is making Ofcom the actual regulator.
So newspapers won't much like this but the warning is it could be worse.