''Minority Report'' (opening June 21) is this movie season's biggest all-star game, teaming Hollywood's most commercially successful director (20 films over 30 years, grossing a total of $2.8 billion domestically) with one of its most bankable stars (23 films, $2 billion). ''How are we marketing it?'' chuckles Tom Rothman, chairman of Fox Filmed Entertainment. ''It's Cruise and Spielberg. What else do we need to do?''

Actually, ''Minority Report'' may require more finesse than that. Based on a 1956 short story by the notoriously trippy Philip K. Dick (whose work also inspired ''Blade Runner'' and ''Total Recall''), this is serious science fiction, a dark, sometimes violent contemplation of a future in which cars have minds of their own, breakfast cereals are packaged in annoying animated boxes, and privacy is so scarce you can't even walk into a Gap without running into a billboard that knows your name and underwear size.

It's also a future in which Cruise's character, Paul Anderton, heads an experimental police squad called Precrime. Tapping into the dreams of a trio of medically mutated psychics, Anderton zips around Washington, D.C., in a jet pack, popping in on people just before they're destined to commit their crimes. All that changes when the ''precogs'' predict his own murderous future and he becomes a fugitive (chased mostly by ''Hart's War'''s Colin Farrell). ''A whodunit before hedidit'' is how Rothman describes the movie.

Cruise, for one, is convinced there's room at the multiplex for a $100 million summer sci-fi thriller aimed at grown-ups, especially one loaded with special effects (like retina-scanning robot spiders) and directed by the guy who all but invented the event movie with a little fishing tale called ''Jaws.'' ''It's a complex story about where our society is going, about what the world will be like in 50 years,'' Cruise offers.

According to Spielberg, he and Cruise had been contemplating making a movie together since David Geffen introduced them on the set of ''Risky Business'' 20 years ago. ''I just knew I wanted to work with the guy,'' Cruise recalls. ''Even back then he was STEVEN SPIELBERG. The guy who did 'E.T.' and 'Raiders of the Lost Ark.''' They considered saddling up for a Western called ''Arkansas.'' And then there was that script about an irresponsible playboy who winds up taking care of his autistic-savant brother. ''I was originally going to direct Tom in 'Rain Man,''' says Spielberg, ''but I had to pull out to do the third Indiana Jones movie.'' (Barry Levinson ended up with the film -- and a Best Director Oscar.)

In a bit of role reversal, it was Cruise who first sent ''Minority Report'' to Spielberg (who usually picks his stars; they don't pick him). Both more or less committed to the project, but at the time Spielberg was about to embark on ''A.I. Artificial Intelligence'' while Cruise was getting ready to shoot ''Vanilla Sky.'' Various drafts of ''Minority Report'' had been floating around Fox for years before Spielberg found time to make his own contribution: He assembled a panel of 28 renowned futurists, handed them keys to suites at Santa Monica's posh Shutters on the Beach, and told them to spend three days brainstorming on life in the year 2054.

''I couldn't use everything they came up with,'' Spielberg remembers. ''The analytical toilet that would catch and evaluate what went down and automatically adjust your diet -- I couldn't find a place for that. But it's just as well. It probably would have gotten me an R rating.'' (In fact, he almost got one anyway; he ended up having to slice a few frames from the opening murder scene and remove some ''F-words,'' as Spielberg puts it PG-13ly.)

Cruise, meanwhile, had his head shaved totally bald for his ''Minority Report'' role. ''I actually helped,'' says Neal McDonough (''Band of Brothers''), who plays Fletcher, a Precrime cop who ends up in a jet-pack chase with Cruise. ''I held him down while his hairdresser shaved it off. It was funny, because the hairdresser was so nervous and Tom kept saying, 'Don't worry. You can't screw this up. You're shaving it all off.'''

''It freaked people out,'' Cruise remembers, when he unveiled the new 'do for the first time. ''Penélope was scared of it. And my kids thought it was weird at first too. Steven offered to let me wear a bald cap, but I wanted to shave it. I really dug it,'' he laughs. ''I just liked the way it felt.''

It doesn't give away too much about ''Minority Report'' to describe a scene in which Cruise disguises himself by injecting a substance into his face that crumples his features into the visage of an old man. It may, perhaps, reveal much more to point out that this is the fifth recent movie in which Cruise has hidden his face either behind a mask or with prosthetics (the two ''Mission: Impossible'' flicks, ''Eyes Wide Shut,'' and ''Vanilla Sky'' are the others). Stranger still, he'll probably be doing it again when David Fincher (the button-pushing provocateur behind ''Fight Club'') directs the next ''Mission: Impossible,'' slated to begin shooting after Cruise completes Edward Zwick's ''The Last Samurai,'' in which he'll journey to 19th-century imperial Japan.

''Holy s---,'' he says after running the numbers in his head. ''That's true. I don't know what that's about.'' He thinks it over for a moment and cracks up. ''They just keep writing this stuff. It just kind of happens. I honestly don't know what it means.''

It'd be tempting to draw facile psychological connections between his compulsion to publicly cover his face and the obvious personal traumas he's suffered over the past year and a half -- so how about we do some of that for a while. There was, for starters, his stunningly abrupt divorce from Nicole Kidman, filed just one month after the couple celebrated 10 years of marriage by reportedly renewing their wedding vows on Christmas Eve, 2000. The reasons for the split remain mysterious -- neither party has dished details -- but it does seem that a thaw of sorts has been declared. ''Nic and I have two kids together, we spent a tremendous amount of our lives together, and you don't forget those incredible times. You move on, but you don't forget.''

Cruise, of course, ended up moving on to Penélope Cruz, his ''Vanilla Sky'' costar -- although the two didn't start dating until after the film wrapped. ''We were friends,'' he explains. ''We talked on the phone. And then it just sort of happened at the end of [last] July. I invited her to go away with me. But I didn't realize it was going to be such a big deal [with the media]. One week the press says we're broken up, the next week we're supposed to be in the Bahamas getting married.'' For the record: Cruise has ''no plans'' to remarry in the immediate future, although he is leaving his options open. ''I'd like to get married again someday,'' he says. ''I'm a monogamist, man. I like being a monogamist.''

The divorce from Kidman and the gossip about Cruz, however, were nothing compared with the news that shook Cruise -- and all of Hollywood, really -- a mere four months ago. Here was the ultimate humiliation, the cruelest twist of fate: At 39, the biggest movie star in the world, the man with the billion-dollar smile, learned he needed braces.

''I was taking my kids to the orthodontist,'' Cruise recalls, ''and he looked at me and said, 'You have a hard time closing your mouth. Your lower teeth are fracturing. I can fix that for you.''' Cruise bares his teeth to show the thin plastic band that's supposed to rescue the most profitable set of choppers in Hollywood history. ''They come off in two months, and then I get a retainer. But it feels good. At least I can close my mouth now. That's a whole new thing for me.''

If a dark thought ever did lodge inside the head of this happy camper, you'd need a mutant precog to pry it out. Even on the cusp of his 40th birthday (July 3), when most men experience their first terrifyingly visceral tingle of mortality (then quickly obliterate the sensation by rushing out to buy a Porsche), he seems entirely comfortable being Tom Cruise. ''It's supposed to be this big transitional thing, right?'' he asks about the big four-oh. ''I guess I don't really get it. I don't think about it much. When I was 22 and I'd be sitting at the head of a board meeting or something, I'd look at these older guys and wonder what it was going to be like. But I always looked forward to it.''