(Rob Carr/AP)

When the 2012 Masters opens next week, much will be the same in Augusta. The azaleas will be blooming. Green blazers, those sartorial markers of prestige, will be worn by the club’s members and be placed on the winner’s shoulders. And the pimiento-cheese sandwiches will still be insanely cheap.

But one thing will be different: The CEO of one of the tournament’s only three sponsors, IBM, is a woman. And as Bloomberg BusinessWeek reports, that puts the heads of the Augusta National Golf Club in a bit of a pickle.

The organization has historically offered its exclusive memberships to the chief executives of its sponsors, which this year would include IBM’s new CEO, Virginia “Ginni” Rometty. (Both Exxon Mobil’s Rex Tillerson and AT&T’s Randall Stephenson are members, as are the last four CEOs of IBM, Bloomberg BusinessWeek reports). Yet the club has never invited a woman to join in its eight-decade history, and has never bowed to the criticism that gets heaped on it for this fact.

If indeed it has been tradition to invite the CEOs of the sponsor companies to join, Augusta National may be hard-pressed to find a good reason not to invite Rometty. She may not be the golfer her IBM predecessors have been — she apparently prefers scuba diving to the links, even if she does play. But Rometty is still the chief executive of a company that undoubtedly supports the Masters not only for the rarified promotion opportunities it offers her brand, or the chance to display its technological prowess (IBM runs the Masters’ Web site, mobile applications and media-center technology), but for the networking opportunity such an exclusive membership brings.

That hardly means Augusta’s powers-that-be will necessarily bend to the pressure. They didn’t in 2003, when the president of the National Council of Women’s Organizations, Martha Burk, sparked a controversy over the club not admitting female members. Nor did they when a list of the club’s all-male members was published by USA Today in 2004. The club’s leadership has said that it may one day invite a woman to join but that, as a private club, it has no obligation to do so.

There are a number of ways Augusta’s leaders could navigate this dilemma, which, whatever happens, will likely occur privately. Patrick Rishe, a sports business professor at Webster University in St. Louis, tells Bloomberg BusinessWeek that they may, like the leadership of other private clubs, be clever in coming up with an exception for women who are sponsors — thereby getting around the controversy without having to change their rules for everyone. It’s also possible they could ask Rometty to join, hoping she’d say no. In 2012, such a membership may not be as desirable for a CEO looking to project a progressive image of her company, especially if she’s not much of a golfer herself.

But I have to think this is a perfect opportunity for the club to quiet their critics without looking like they’re doing it on someone else’s terms. A place as steeped in history as Augusta National gets to stick with one of its values — tradition — and invite a sponsor CEO to join just as they have in the past. In the process, they make themselves appear more inclusive. And they won’t look like they’re bending to the pressure of accepting a woman just to quiet their critics. Augusta’s leaders have said in the past they’d be open to inviting a female member in the future. If the CEO of one of this country’s most enduring corporations, which also happens to sponsor the tournament, isn’t that woman, who is?

More from On Leadership:

Masters might be facing a gender problem. Again.

JetBlue’s pilot fiasco

How to completely destroy an employee’s work life

In basketball, one rule to wring them all

View Photo Gallery: Washington Post readers respond to the article “How to completely, utterly destroy an employee’s work life,” and share their own “advice” for making employees miserable.

Like On Leadership? Follow us on Facebook and Twitter:

@post_lead | @jenamcgregor | @lily_cunningham