David Cameron is a flip-flopper. He is therefore likely to be a successful prime minister. Last week, having insisted for years that his only motive in employing a press secretary was as a rehabilitation of offenders scheme to give a second chance to Andy Coulson, he accepted that the urchin would have to seek a third chance elsewhere. It was Coulson's decision, we are told, but I get the impression that Cameron did not fight too hard against it. He saw the logic of it. So did the Leader of the Opposition's office. Ed Miliband went on television to say that "there are questions about David Cameron's judgement", which is French for: "Oh no, he has shot my fox."

There are, in fact, questions about Cameron's judgement, but the answers are not ones that the Labour leader wants to hear. One is that Cameron has a sinuous feel for the intangibles of politics. Another is that he's not afraid of U-turns. This isn't really a U-turn in the classic sense of policy "A" being replaced by policy "Opposite-of-A". There have been a string of those too, and they also tell us much about Cameron's character.

But first the Coulson business. The "judgement" cliché to which Labour resorted means, "This proves that you didn't ask the right questions when you hired him." My understanding is that Cameron thought such cross-examination beneath his dignity, but was forced to ask Coulson before he gave evidence to a select committee of MPs if his stint as editor of The News of the World might come back to bite him. Coulson may have told him what he told other confidants, namely that he was sure there was "no paper trail". (James Hanning, Cameron's biographer, has more details in his article today)

That does not mean Cameron necessarily lacks judgement. There is something in his lack of curiosity that fits the picture that is emerging of the kind of prime minister he is. The fact of the coalition has helped him greatly, but he is a prime minister who seems to float above the fray.

This has advantages for image management. He can pose as the collegiate team leader – and, incidentally, head off all the nonsense about elective dictators riding roughshod over the rules of Cabinet government laid down by Magna Carta, which dogged Thatcher and Blair. And he has some distance from unpopular decisions, with tuition fees the most striking example so far.

But he can also descend from Mount Olympus when he needs to, to sort out problems that escape from the control of departmental ministers and threaten to make him personally look bad. Sometimes these excursions from above the snow line can be lightning fast. Last August, he reversed a decision to abolish free milk for under-fives so quickly that David Willetts, the universities minister, was on television defending the decision while the Prime Minister's spokesman told journalists that it was not going ahead.

Usually, U-turns took longer, as Coulson assessed the durability of a negative storyline and its capacity to harm his boss. It took several days for Cameron to admit that hiring a photographer on the public payroll had sent the "wrong message" at a time of fiscal stringency. It was a sensible retreat. The phrase "vanity photographer" was half-way into the car-following-bicycle myth-making machine before Coulson threw the reverse switch.

Then came the U-turns on free books for young children (the Booktrust scheme) and the School Sports Partnership. Both cuts threatened the image of Cameron, the family man who wants to shield children from the worst effects of the "inevitable" tough decisions that he has to take as father of the nation. The sums of money involved were trivial, so down from the mists again came the Lord Protector.

There is a petulance about Cameron, and it sometimes surfaces on these occasions, as it did at last week's Prime Minister's Questions. He does not like his self-image as a decent person to be questioned. What he did not say, but seemed to think, when Ed Miliband surprised him with questions about the NHS, was: how dare he doubt my good intentions, when I relied on the NHS to look after my disabled child? He was quick to react, too, to Thursday's accusation from a parent that he had broken his promises on respite care for severely disabled children, which ran in the mass-market press.

That, I suspect, explains at least some of Cameron's loyalty to Coulson. As is often the way with these things, we can see the point of Coulson more clearly now that he is going. For much of his time at the Conservative leader's side, Coulson has seemed more like a source of tension with Steve Hilton, Cameron's strategy adviser and genius of the sunshine-and-socially-liberal side. This side seems – I have written that column myself – at odds with the patriot-family-discipline themes preferred by Coulson (although there's no necessary contradiction, if you think about it). But that is to misunderstand Coulson's value to Cameron.

Coulson was good at judging when to kill bad news stories about his principal. The U-turns of the past eight months were more about preserving Cameron's personal image than that of the Government as a whole. And they are the skid-marks of strength, not weakness.

Cameron's willingness to drop policies at the first whiff of cordite sometimes made him look flaky in opposition, but it makes him a formidable prime minister. Yes, eventually such reactive flexibility and touchy petulance might come to be his undoing, but that could be years away. For the moment, quick flip-flops on small issues mean that they do not distract from the big picture. No wonder Cameron thinks highly of Coulson. He was good at keeping the Prime Minister's name away from toxic media stories – and in the end that included himself.

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