“Mad Men” fangirls and -boys clapped their little hands in glee Tuesday when AMC announced that it had “officially authorized” the production of a fifth season on the sumptuous period drama — ending speculation that the show might be canceled.

True, to-die-for-in-those-suits Don Draper won’t be back until early 2012 — several months later than the show’s previously expected fifth-season debut in the summer of ’11, but heck — it’s cable. That’s how they roll.

But those boys and girls might want to hold off on those We Don’t Have to Imagine a World Without Don Draper After All candlelight vigils of thanks, and mull for a minute what their mothers taught them about being careful what they wish for.

Because there’s a line in AMC’s announcement that goes like this:

“While we are getting a later start than in years past due to ongoing, key non-cast negotiations, ‘Mad Men’ will be back for a fifth season in early 2012.”

By “key non-cast negotiations,” AMC means “Matt Weiner.”

Weiner created “Mad Men”; he is the show-runner. And, for better or for worse, he is its heart and soul.

“Mad Men” without Matt Weiner could be like “Lost” without Damon Lindelof.

Or “The West Wing” once Aaron Sorkin left — remember how grim that got? Kinda like that.

Although AMC’s contract with Lionsgate, the company that produces “Mad Men,” always ran through a fifth season — AMC said in Tuesday’s announcement that it had “triggered our option with Lionsgate” — Weiner does not have a contract to work on the show for a fifth season.

Here’s what’s holding up that contract:

Weiner has a deal on the table that’s worth $30 million over three years. That would make him one of the wealthiest show-runners in all of TV — broadcast or cable.

AMC wants to help pay for Weiner by adding another ad break into the show, without growing the show’s overall length. Those minutes would have to be trimmed from the show’s content.

Last time the sides sat at the bargaining table, AMC added another ad break, too, according to a source with knowledge of the negotiations who did not want to be identified because you never know who your next boss is. That time, AMC finally agreed to add two more minutes to the show’s overall length.

Last season, the show ran about 47 minutes per episode. At 45 minutes, it would come closer to being like a broadcast TV drama — those typically have about 42 to 44 minutes of actual drama per hour of your life you’re not going to get back.

There’s also banter being exchanged between Weiner’s camp and AMC’s about whether they’ll increase the amount of product integration in the show and, as the source with knowledge of the kerfuffle put it, whether AMC would start allowing advertisers to advertise their advertisements. That’s kind of a hilarious point of contention, given that “Mad Men” is a drama about the epicenter of crass American commercialism — Madison Avenue — in the ’60s.

Weiner is also balking at suggestions that he cut costs on the show — which runs a reported $2.5 million per episode — by scrubbing a couple of members of the ensemble cast, which, in fairness, is pretty big.

Tuesday’s announcement strategy is similar to the tactics that the network employed two years ago, when it was also slogging through acrimonious contract talks with Weiner to re-up him for more seasons on the show.

Entertainment-industry trade papers and fangirl bloggers have been all atwitter over the “Mad Men” sitch for several days now. During that period, AMC insiders have been holding firm to their position that the offer on the table for Weiner is plenty rich, and that such issues as show length, number of ad breaks and product integration should be handled by the network, not a series creator. AMC sounds just like — a broadcast network!

AMC declined to comment about the Weiner negotiations beyond its Tuesday announcement. Weiner, meanwhile, is on a ski vacay with his family, his reps said, and could not be reached at press time.

“Mad Men,” winner of the best drama Primetime Emmy Award three years running, put AMC on the map in a big way, back in the summer of 2007.

AMC’s parent company, Rainbow Media, which, in turn, is a division of Cablevision — isn’t vertical integration a peach? — reportedly is preparing to spin off AMC as part of a new stand-alone unit. It would also include IFC, WE and Sundance Channel.

AMC would appear to be the anchor department store in that shopping mall. That may explain why AMC seems hellbent on squeezing every dollar it can out of “Mad Men’s” fifth season.