So how effective might it be, this new press watchdog, this "Son of PCC" as William Lewis, the former editor of The Daily Telegraph, was anxious to name it?
Certainly there is a will – expressed by various senior Fleet Street figures yesterday – to give a successor body to the Press Complaints Commission a host of powers which might ensure something positive comes out of the shameful phone-hacking affair. That might mean the power to impose fines or issue kitemarks which show a publisher is committed to a set of standards. Lewis himself advocated that a new body might have the right to exclude non-signatories from the official circulation figures, the "currency" that news organisations use to justify advertising rates.
Lord Justice Leveson did not seem convinced but it was clear he was anxious to hear Fleet Street's thoughts on how it might clean up its gutters. After listening to the tawdry evidence of phone hacking and other press malfeasance, the judge is looking to the future. "I'm very keen that the industry has some ideas provided the industry accepts that they have got to work not only for the industry but for me," he said, adding, "by me – I mean the general public."
As he shot the breeze with the likes of Financial Times editor Lionel Barber and Telegraph Media Group chief executive Murdoch MacLennan, he thought aloud of a new watchdog with an arbitration arm that could speedily and inexpensively rule on disputes.
Perhaps some critics of the British press might be disappointed by Leveson's appetite for a dialogue. The inquiry drew criticism for the failure to interrogate The Sun more thoroughly over such matters as the Hillsborough disaster. But although Lord Justice Leveson said he "understood" why newspapers were afraid of state regulation and acknowledged the disadvantages the press faced in comparison to unregulated online publishers, he signalled he will not be happy with anything less than radical reform of press regulation. "I'm not going to call it the Son of PCC," he told Lewis, "because that suggests a little tinkering will do."