I think Paramount scooped up a bargain when it paid a reported $4 million for Sundance fave “Like Crazy.” It might be the finest picture of its kind since “Once.” I can easily picture about a half a million high school and college girls taking to Twitter to declare this their favorite. Movie. Ever.

Director Drake Doremus, who was here last year with an amusing slacker movie called “D—–bag,” shoots in a cinema-realite fly-on-the-wall style (the cameras are often hand-held and the sound mix is a bit naturalistic, i.e., somewhat garbled, in the manner of a Robert Altman movie) that can be annoying but is well suited in making this movie seem like it’s just looking in on a couple of nice young people and the ups and downs of their love affair.

He (Anton Yelchin) is Jacob, a budding furniture designer in L.A. who meets Anna (the adorable Felicity Jones) in a class. They pass each other sweet notes, listen to Paul Simon and trade I-Love-Yous. But Anna is English, and must leave the country before her visa expires. Instead, she hangs out with Jacob all summer, meaning she is in violation of visa policy and is going to find it very difficult to get back in the US once she goes back to London, which she does after the summer. Now they must try to keep a long-distance romance going.

The film is much lighter, warmer and more romantic than “Blue Valentine” and much less silly and frantic (without the look-at-me-I’m-directing quality) than “(500) Days of Summer.” The fragile, winsome Jones, who still has a slight air of childhood about her, has major star wattage, though the relaxed and amiable Yelchin, who plays his role very quietly, never quite seems like the kind of major charmer he would have to be to attract the beautiful women he does.

The movie is an unabashed romance, full of tender moments and beautifully realized scenes (I particularly loved a montage of the two leads lying in bed and an even more imaginative sequence in which one of them appears to spend six months waiting in an airport). It’s blissfully sweet (not syrupy; not saccharine) and its running motifs — particularly a chair that is, believe it or not, the third most important character — are lovely. A bracelet reads “Patience” — isn’t this the most elusive quality in the world when you’re about 22?

Like “Once” and the French New Wave film “A Man and a Woman,” the entire movie stays up close with its two leads (though there are other characters) to bring across a sense that for them, there is nothing else in the world but each other — at least when they’re together. As in the two earlier films, there isn’t a lot of dialogue because there doesn’t need to be, although the lines are often witty. “In London,” says an exasperated Anna to her parents, “you can just be drinking all the time.” “Yes?” says his Scotch-loving father, puzzled.

I haven’t quite decided whether I like the film’s ending, which will perhaps lead to a lot of post-movie discussion among desperate young lovers, but overall “Like Crazy” is an exhilarating blast of young love’s crazy glory.

I think it’s going to be a hit with girls and women, particularly young ones. It could be an even bigger hit if it achieves a PG-13 rating that will open the door to a lot more customers, and that could be accomplished if a brief sex scene were made less explicit and four (I think) uses of the F-word were to be cut. (All of this could then be restored to give some sizzle to the “unrated director’s cut”).