Now that the dust has settled a little from last week’s Iowa caucuses, we can see that while they didn’t give Mitt Romney everything he wanted, they have certainly reshaped the Republican race in a way that’s highly favorable to him. Three things in particular must make Romney very pleased with the Iowa result.

First, he won — incredibly narrowly it’s true, but a win is a win, and for most of the last six months any sort of Iowa win seemed highly improbable for Romney. Among other benefits, winning should sink the campaign of Jon Huntsman, Romney’s only moderate rival, whose strategy depended on Romney being badly hurt in Iowa. (Huntsman didn’t campaign in Iowa, but even so the fact that he received less than 1% must be pretty galling.)

Second, Romney has effectively knocked out Rick Perry, who had the potential to be his most dangerous opponent — being well-funded and experienced, running to Romney’s right but broadly acceptable to the party establishment. Perry might have survived a fourth-place finish, but fifth, with just 10.3%, looks fatal. Officially he is staying in the race (and Nate Silver, for one, is refusing to rule him out), but Romney can stop worrying about him.

Michele Bachmann, who finished a distant sixth on 5%, has folded her campaign, but since Romney clearly had her measure anyway that is less obviously a plus for him.

Third, the Ron Paul surge has been halted; Paul’s 21.4% put him a very respectable third, but having led in the polls a week earlier that’s not good enough. Paul was never likely to be the nominee, but he had the capacity to be a considerable irritant for Romney: that capacity, while not eliminated, has been significantly reduced.

There were two notable things that made this less than a perfect result from Romney’s point of view. One is that he failed to kill off Newt Gingrich, whose 13.3% was a big comedown from a month ago but enough to keep him alive at least until South Carolina on 21 January.

The other thing is that Romney failed to prevent the hard-right vote from rallying behind a single candidate. Former Pennsylvania senator Rick Santorum turned out to be the one who peaked at the right time, after being ignored by everyone until the last couple of weeks, and came within eight votes of beating Romney. He and Gingrich are now Romney’s only serious rivals.

You can have a go at why Santorum might have been thought preferable to his fellow-extremists (Noah Millman did so last week), but it would be fundamentally irrelevant. He surged because he was the last one left standing; as Ezra Klein puts it, “Santorum was unable to attract significant support until the very end, when the anti-Romney vote literally had nowhere else to go. If he had been a better candidate, he would have crested earlier.”

In other words, while it would be best for Romney for the Tea Party vote to stay divided, if it’s going to unite behind one opponent then Santorum is about as weak a choice as there is. Grassroots discontent with Romney still gives him a faint chance, but even the craziest of Republican voters must shiver slightly at the thought of facing Obama with Santorum as their standard-bearer; it would make 1964 look like a cliffhanger.

Yet Gingrich and Santorum are now competing for the anti-Romney mantle, each hoping to reduce the other to irrelevance by beating him this week in New Hampshire (it’s accepted that no one can beat Romney there).

Making things more difficult for both of them is the fact that Paul and Huntsman are relatively strong in New Hampshire, and could well finish in second and third place. That will make it even harder for anyone else to garner the momentum (and therefore cash) to overtake Romney in South Carolina, which looks like being the right’s last stand.

Amid the criticisms of the Iowa caucuses for their unrepresentativeness and just plain weirdness, it’s often pointed out that their predictive power is quite poor – it’s not unusual for the eventual winner to do badly there. (Bill Clinton managed only 3% in 1992.) But their real role is negative; typically they winnow out the field and clarify the remaining choices. This year they seem to have performed that role very effectively.

There are now only three viable candidates in the field, and two of those are rank outsiders. There’s not much doubt Mitt Romney will be the nominee but everyone’s hoping to keep the excitement going just a little bit longer.