It centred on four ex-Special Ops who were now soldiers of fortune, fighting moustachioed crooks by day, and at night, trying to figure out how they can prove that they're innocent of the crime that has them branded as war criminals.
And just to prove that they're not the baddies of the piece, Colonel John 'Hannibal' Smith (George Peppard), Lieutenant Templeton 'Faceman' Peck (Dirk Benedict), Captain HM 'Howling Mad' Murdock (Dwight Schultz) and Sergeant First Class Bosco Albert BA 'Bad Attitude' Baracus (Mr T) would not only use their considerable warfare skills for good, but they would also make sure that the only violence on offer was purely of the cartoon variety.
Cooper takes on the Faceman role in the movie version, with District 9's Sharlto Copley as Murdock, martial arts star Quintin Jackson as BA, and our own Liam Neeson as the relatively wise Hannibal.
"We certainly wanted to make sure we got the tone right here," says Cooper. "There is that cartoon violence, but there's some good old-fashioned thrills and spills alongside all the humour, too. You have to include the humour and the action, but, you know, with a certain degree of self-awareness. Audiences are very literate in not just film but pop culture in general, so, they're ready for us to have a little fun with the format here. I think the film is a hoot . . ."
You're not just saying that because you're in it, I hope. "Absolutely not! I'm not that kind of guy . . ."
The kind of guy Bradley Cooper is -- if his army of admirers are to be believed -- a George Clooney-in-waiting. Ever since The Hangover made the 35-year-old, Philadelphia-born actor a bona-fide star, an army of (female) fans have guaranteed that even a so-so movie such as Valentine's Day scores big at the box-office. And the so-so big-screen adaptation of The A-Team just might follow it.
Suddenly, the years of playing support, in the likes of Wedding Crashers, Failure To Launch and Yes Man, have proven worthwhile. Right?
"Right," smiles Cooper. "But it's not like all those years were just some kind of waiting game. Each new role, you give it your best shot, and hope that something special is there at the end.
"I guess the one big advantage of having some real success in The Hangover is that I now have more choices. But I'm still having to take my chances.
"Movies like The Hangover are very rare in this business, no matter how big you are."
Indeed. In Hollywood, there are few movies such as The Hangover -- where the right script, the right director and the right cast all end up on screen together -- and far more movies such as All About Steve. And Case 39,to name the two duds Cooper found himself in after his big breakthrough. "You see what I mean?" he laughs. "You never can tell. You give it your best shot, and that's all you can do. Who knows how the film is going to turn out? And how the industry is going to react to it? Sometimes, great movies get buried because it just wasn't the right time."
And on other occasions, it's simply because the movie isn't all that good.
"True, true, but I don't think you can completely dismiss All About Steve or Case 39. There was some interesting stuff going on in both of those movies, and if they didn't quite work for audiences, each was, in its own way, a good shot at making a good movie."
For Cooper, these days, it's all about choosing carefully. There's a second Hangover in the works ("I don't think we'd dare go there unless we had a script we all loved, and laughed out loud at"), but, other than that, it's a game of wait-and-see.
Our times nearly up, so, let's talk about sex, baby. Somewhere in Cooper's family tree, someone having sex was Irish. Which explains everything.
"I think I got a really cool mix, actually," smiles Cooper. "I got some Italian blood in there, I got some Irish, and I grew up in Philly. Being brought up a good Roman Catholic, of course I've got passion coursing through my veins.
"All those repressed sexual urges growing up, brought on by that wonderful Catholic guilt -- it made me the man I am today . . ."
The A-Team opens on July 28