David Cameron came to the House of Commons on Wednesday with a clear aim. He wanted to close a chapter in the phone-hacking crisis before the summer recess. With his own credibility under challenge, with unanswered questions proliferating and with parts of his party increasingly uneasy, the prime minister returned from Africa to try to reassert a grip he had lost since setting up the Leveson inquiry on 13 July. In party terms, his sharper expression of regret over the hiring of Andy Coulson and the announcement of broader terms of reference for the inquiry satisfied Conservative MPs. They rallied behind Mr Cameron, began to turn the heat on Labour, and will head off on holiday more confidently. But neither they nor Mr Cameron should get cocky. The prime minister left important questions unanswered. And he has set in motion processes of inquiry into a still unfolding story which, at the very least, will change the way that he and the rest of us do politics and may yet force him into some very tight corners and do lasting harm to his reputation, too.

It is easy to claim, as Tory backbenchers concertedly did, that the public is ready to move on. But the unanswered questions cannot be just wished away. Mr Cameron's conduct and judgment remain at issue, whether Conservatives like it or not. By his own admission, the PM has had 26 meetings with News International executives in 15 months at a time when Rupert Murdoch's UK operation has been focused on taking full ownership of BSkyB and during which NI's phone hacking has been an open sore. In a carefully parsed remark that echoed Bill Clinton's denials of sex with Monica Lewinsky, Mr Cameron said that he "never had any inappropriate conversations" with Mr Murdoch or his minions. But that is an awful lot of meetings with important friends and contacts in which to avoid subjects that were uppermost in NI minds. Given seven chances to deny he had discussed the BSkyB deal, he failed to do so. The inference is clear. And so is what it says about Mr Cameron's judgment.

Nor can Mr Cameron wish away his misjudgment over Andy Coulson, much as he may now wish to put more distance between himself and his former communications chief. The evidence that Mr Cameron operated in, at best, a bubble of denial of the Coulson problem continues to fester. The prime minister was warned, directly and by intermediaries, about Mr Coulson's involvement with phone hacking while at the NoW. Downing Street's refusal to give details about the firm which vetted Mr Coulson only adds to the impression of casualness towards matters that could and should have been addressed more seriously. Mr Coulson's security clearance, it now emerges, was not as wide as he might have expected it to be. Did no one ask why? Mr Cameron's chief of staff may indeed have acted properly in keeping himself and the prime minister behind a cordon sanitaire on phone hacking. But it added to the failure to address the Coulson problem all the same. These are problems deferred, not problems addressed or solved.

The defensiveness over Mr Coulson and No 10's other NI links is a striking contrast, perhaps suspiciously so, with the radical approach and positive tone Mr Cameron adopted elsewhere in his statement. It is wise to broaden the inquiry to cover all police forces and to look at possible criminal activities by other forms of media. The appointments to the Leveson panel are well balanced. And Mr Cameron's healthy instinct for transparency in other contexts was underlined by his announcements that politicians should have no future role in media mergers and that police chiefs could in future come from outside the service. He is right to want the civic catharsis of which he spoke. But we will not get this desirable outcome while the curtains remain pulled shut over so many so important unanswered questions.