Cross my heart, we’re not making this up, even though it flies in the face of conventional wisdom, anatomical reality and the billions of dollars raked in last year by Victoria’s Secret: Wearing a bra might actually make your breasts sag.

At least that’s the conclusion drawn by Jean-Denis Rouillon, a professor at the University of Besançon in France. For the past 15 years, Rouillon has been diligently taking a slide rule and caliper to the breasts of 320 women, ages 18 to 35, to measure any changes, particularly the relationship of the nipple to the shoulder. (To the surprise of no straight man with a pulse, he has said that these results are preliminary and that further research is needed.)

The sports science expert told France Info radio that “bras are a false necessity,” and that “medically, physiologically, anatomically — breasts gain no benefit from being denied gravity. On the contrary, they get saggier with a bra.”

Whether the French study proves credible — it’s yet to be peer-reviewed — it prompts questions about anatomy, culture, marketing and history. Was the bra invented with women’s physiological health in mind? Or was it rooted in cultural prudishness — a way to keep the girls corralled?

Highbeams and lowbeams

More the latter than the former, said Jean McElvain, assistant curator at the Goldstein Museum of Design at the University of Minnesota, which has an extensive collection of lingerie. But both reasons take a back seat to a third: Style.

“The silhouette of fashion is really dictating what you need under it,” McElvain said. “The 1940s saw a major de-emphasis because of shoulder pads. The 1950s saw the return of the hourglass figure, with bullet bras.” [Think: Joan “Mildred Pierce” Crawford and Joan “Mad Men” Holloway, respectively.]

With the 1960s came Rudi Gernreich’s “No Bra Bra,” part of the Goldstein’s collection. “It’s semi-transparent, with no padding,” McElvain said. “After the structure of the 1950s, it was supposed to get women around to the idea that they don’t need padding. Really, you just need something to keep them in place.”

McElvain doubts that women will pay the French study much heed. “If someone said, let’s not wear bras anymore, it would take many women a long time to stop wearing them,” she said. “Seeing nipples, even as impressions through a shirt, still seems an impropriety.”

That assessment jibes with the experience of one woman whose bosom means business.

When Queenie von Curves, a burlesque performer in Minneapolis, heard about the anti-bra study, “my first thought was, ‘I wish,’ ” she said. “I really can’t go out in public without a bra, unless I wear a top that can restrict them from moving freely. In most avenues of society, with just a T-shirt, I would be considered inappropriate.”

Call it modesty or hewing to social norms, wearing a bra also pays the bills.

The Center for Talent Innovation surveyed 4,000 executives about gender stereotypes and reported in a recent AdWeek that on the issue of a woman not wearing a bra, three in four women executives considered that a blunder — although among male bosses, just under half disapproved.

Anatomy is destiny

Given the quest for a comfy bra, it’s worth remembering that women once welcomed brassieres. The main reason: They weren’t corsets.

In their mostly tightly laced forms, corsets could fracture ribs, puncture lungs, restrict breathing and damage internal organs. A bra offered relative freedom, but medical advantages paled over the years in the face of promises to “lift and separate.”

According to the French study, that “lift” allows ligaments that support breast tissue to become weak. Rouillon said that women who did not wear bras had, on average, “nipples [that] lifted on average seven millimetres in one year in relation to the shoulders,” according to an account in the Connexion, France’s English language newspaper. (That’s about a quarter-inch.) Thus, he concluded, breasts would gain more tone and be better able to support themselves if no bra was used.

Hmmm. So how does female architecture actually work? Dr. Paul Tran, an associate consultant in plastic surgery at the Mayo Clinic, provided an anatomy lesson.

“Breast tissue develops over time,” he said. “This glandular tissue is very dense, but then as people age, it turns into fatty tissue which is much less dense.” Thus, breasts begin losing some of their perkiness.

Breasts also are supported by Cooper’s ligaments, connective tissue that essentially suspends breasts from the clavicle. “The way we’d remember them in med school was by calling them Cooper’s droopers,” Tran said, explaining that these ligaments do stretch over time from factors such as age, weight changes, number of pregnancies, hormonal changes and smoking.

Sagging, he said, “is an inevitability. Cooper’s ligaments aren’t discrete, like an ACL, but are all these tiny ligaments throughout the breast tissue. There’s really no way to tighten them.” Exercises to strengthen pectoral and back muscles may have an effect, but mostly because they result in improved posture.

The show must go on

Queenie von Curves, whose real name is Renata Shaffer-Gottschalk, has looked at bosoms from both sides now. As a company dancer with Ballet of the Dolls, she straps hers into submission with a heavy-duty sports bra, “and I’ve even been known to bind them with an ace bandage,” she said. “It’s a matter of comfort, just to be able to do the choreography.

“But in burlesque it’s, ‘How can I make these even more obvious to the crowd?’ ”

Happily, she’s found that her stage work holds some solution to the perils of sagging as she’s learned better techniques for manipulating her pectoral muscles.

“I feel I’ve evolved better muscles through tassel-twirling,” she said. “I’ve actually noticed a lift.”