This fact-based tale of man helping mammal is, like its predecessor “Dolphin Tale,” manipulative in the extreme but surprisingly enjoyable nonetheless.

The picture is based—loosely, of course—on the effort the effort called “Operation Breakthrough” to rescue three whales trapped off the northern coast of Alaska by arctic ice in 1988. The animals—two adults and their offspring, in this telling nicknamed Fred, Wilma and Bam-Bam—were discovered using a small hole in the ice to breathe, doomed to perish when that opening was covered as well. Here, the story is broken by likable Anchorage TV reporter Adam Carlson (John Krasinski), whose piece is ultimately picked up by Tom Brokaw and turned by the media into a national sensation.

Adam was once romantically involved with Greenpeace activist Rachel Kramer (Drew Barrymore), who’s best known for opposing the plans of big oilman J.W. McGraw (Ted Danson) to exploit protected Alaskan territory from drilling and who now arrives to encourage local wildlife official Pat Lafayette (Tim Blake Nelson) and Alaska’s Governor Haskell (Stephen Root) to save the whales. Meanwhile among the national press that show up to cover the event is Jill Jerard (Kristen Bell), a hot blonde whom Adam helps, seeing her a possible ticket to a career in Los Angeles.

But the cast of characters is far larger than that. There are members of the indigenous Inuit tribe, who plan to harvest the whales until their revered leader—who might be thought of as the Alaskan equivalent of Chief Dan George from “Little Big Man”—persuades them that killing the critters would be a disaster and they should contribute to the rescue effort instead. (He also has a cute, “modern” grandson whom Carlson has befriended.) There’s Kathy Baker, as McGraw’s canny wife, who uses reverse psychology to persuade him to lend his ice-breaking barge to the effort as a cunning PR move. That decision leads to the entrance of a couple of Alaska National Guard helicopters, commanded by Col. Scott Boyer (Delmot Mulroney), who’s tasked with towing the huge vessel across the ice to the site of the ongoing drama. And watching from Washington is presidential aide Kelly Meyers (Vinessa Shaw), who sees the rescue as a chance to refurbish the administration’s environmental reputation and gets President Reagan directly involved, to the extent of even requesting intervention by a Soviet ice-breaker. That makes for a literally crashing finale, though there are some tears to be shed before the shouting. There are also some laughs courtesy of James LeGros and Rob Riggle as a couple of goofy inventors who come from Minnesota with a ice-melting device that, wonder of wonders, actually works.

“Big Miracle” is obviously a very calculated feel-good movie that will certainly join “Free Willy” among whale-philiacs. But the curious thing about it is that when you look at the motivations of most of the characters, they’re hardly as white as the Alaskan snow. Everybody has some ulterior motive in mind—whether it’s political strategy (national or international), professional advancement, or simply varnishing the reputation of your people or your company. (Even that little boy uses the event as a way to make money.) Yet the message is that in the end everybody sets aside their petty concerns and comes together in a common purpose. That at least gives the movie a bit more shading than usual in such fare.

The picture also benefits from a great cast. Only Barrymore disappoints, coming across as too shrewish and abrasive, though to be fair that’s how the character is written. Bell is somewhat stiff, but Krasinski brings his “Office” charm to the party, and Danson, Nelson, Mulroney, Root, Riggle and LeGros all contribute nice comic turns. Director Ken Kwapis keeps things moving nicely, and cinematographer John Bailey uses the Alaskan locations to good effect. Technically all is well, with the animatronic whales convincing substitutes for the original. And there’s a clever smattering of found footage to make things chronologically convincing, both excerpts from the networks’ nightly news programs and brief clips of politicians (although, as usual, the archival shots of Reagan don’t match terribly well with bits featuring a stand-in). For once the “what happened next” and “real people” clips at the end are interesting, and one cleverly engineered combination of the old and the new places Krasinski in the frame with a famous Alaskan personality in her younger days.

It’s a minor miracle that “Big Miracle” is as pleasant as it is.