The title of this earnest family movie is a play on words, since it could also be spelled as “Dolphin Tail.” (A book on the real-life incident that inspired it is in fact titled “Winter’s Tail.”) It’s the story of a dolphin, eventually called Winter, whose tail had to be amputated after becoming infected, but was outfitted with a prosthetic replacement that allowed her to survive by using it to swim properly. And the injured dolphin plays herself.

Of course while that might make for a nice thirty-minute documentary, it’s hardly sufficient for a feature film. So the focus is put on young Sawyer Nelson (Nathan Gamble), a fatherless, friendless boy who finds—and aids—the beached animal after it’s washed up ashore, tangled in a fishnet. After it’s taken off to the Clearwater aquarium/hospital where it’s tended to by dedicated widower Dr. Clay Haskell (Harry Connick, Jr.) and his perky young daughter Hazel (Cozi Zuehlsdorff)—both of whom live with his father Reed (Kris Kristofferson) on a nearby houseboat—Sawyer finds his way there and a purpose in life when the dolphin takes a special shine to him. He becomes an integral part of the animal’s care team, despite the fact that his role means he’s in danger of failing summer school, something that worries his mom Lorraine (Ashley Judd).

But that’s not enough story for scripters Karen Janszen and Noam Dromi. They add a complementary human plot about Sawyer’s beloved cousin Kyle (Austin Stowell), a swimming champ who joins the army and comes back from Afghanistan a despondent amputee. Naturally he’s helped out of his depression and self-pity by getting to know Winter, and when it becomes clear that the way that Winter has learned to swim without a tail is endangering her life, Sawyer approaches avuncular, bromide-filled Dr. Cameron McCarthy (almost inevitably, Morgan Freeman), who constructed Kyle’s prosthetic leg, to try something never attempted before: making an artificial tail for her.

But even all that doesn’t exhaust the screenwriters. They find room not only for a financial crisis that threatens the aquarium’s survival—Frances Sternhagen plays the president of the place’s governing board who can seen no way out but selling the land to a hotel magnate—but a hurricane that nearly wrecks the facility. Then there’s the big finale that includes an Internet campaign and a water carnival.

But despite a surfeit of plot points, the picture is kept on an even keel by actor-director Charles Martin Smith, who doesn’t rush and lets the actors (including the dolphin) breathe. And he has a cast aboard that’s much stronger than what you’d expect in such fare. Freeman, of course, is utterly reliable in this sort of feisty but warm role, and it’s good to encounter Judd in a part that doesn’t require her to run around in action-woman mode, chasing criminals or fleeing killers. Kristofferson adds his crustily lovable shtick to the mix, and old pro Sternhagen manages to look genuinely concerned. And Connick has at least lost the deer-in-the-headlight look he used to sport on-camera. Even Stowell brings a touch of real emotion to Kyle.

But of course it’s the kids and the dolphin that really matter. Winter does everything asked of her, and Zuehlsdorff is charming. But’s it’s Gamble who really proves the linchpin. Under Smith’s sensitive direction, he captures both the boy’s gravity and his exuberance when he finds a purpose. He shows some of the same quality that Henry Thomas did in “E.T.”

Together these three—the youngsters and the dolphin—show that there’s life left in the old “Flipper” formula yet (despite the disaster of the 1996 remake of that movie with Elijah Wood). Of course, whether a kid-targeted movie like this, which eschews the frenetic action and potty humor that most “family” movies opt for nowadays—can prosper in today’s multiplex marketplace remains to be seen. But on its old-fashioned terms, this well-made, gently comforting modern version of a 1950s live-action Disney movie is like a refreshing sea breeze in a maelstrom of fart jokes and CGI mayhem. A pity that the makers made a concession to today’s tastes by going the 3D route. Except for a couple of moments obviously manufactured to play to it, the format adds nothing to the picture whatever—it even detracts from Karl Walter Lindenlaub’s cinematography by darkening the visuals, as usual.

But since that’s one of the movie’s only concessions to today’s fads, we can live with it.