Here’s a fun drinking game for Paris tourists: Hunt for Overnoy. In every restaurant, bar and wine shop, request bottles of the legendary Jura winemaker’s incredibly limited Arbois. Every time someone laughs in your face or insists that no stock remains, take a drink of something else.

I spoke to a bevy of sommeliers and restaurateurs recently about wines they have trouble keeping in stock, and Pierre Overnoy was the name on every tongue. Chef Rodolph Paquin, the jolly, giantesque wine hoarder behind Paris restaurant Le Repaire de Cartouche, told me that his allocation of the domaine’s Vin Jaune is down to just one bottle per year.

Vin Jaune is a costly, immortal, amontillado-like white wine from the savagnin grape aged in barrel beneath a veil of yeast for a minimum of six years. But it’s Overnoy’s less exotic—though no less impressive—whites and reds whose approachable pricing renders them ripe targets for what is has come to be called “cherry picking.”

Cherry picking means to plunder a wine list for its rarest and most renowned bargains. Cherry pickers will order a rare bottle, and then to keep ordering it all night, exhausting the stock. The practice is considered bad form, since rare and renowned bargains are precisely the wines that confer a glow of good value and prestige on the rest of a list’s contents. Wine geeks from San Francisco to Tokyo to Paris cherry pick anyway, since concern for the integrity of someone else’s wine list tend to fade, universally, after the second bottle.

It’s why Overnoy has disappeared from many Paris wine lists, along with most back-vintage natural wines. Without enough natural wine to satisfy rising demand, and 30 million tourists passing through the city each year, Paris’s wine destinations are increasingly unabashed about discouraging cherry pickers, a development which, counterintuitively, makes many of these restaurants unlikely places to enjoy the most famous natural wines.

The simplest defense against cherry pickers, practiced at wine-shop-slash-restaurant Le Verre Volé and celebrated Belleville bistrot Le Baratin, is to have no wine list at all. Ostensibly this is to ensure that each table arrives at the optimum wine choice. In practice, it also ensures that clients are screened before each wine sale.

“Merely asking for a wine is not enough to have it served to you; we have a nose also for recognizing good clients,” says Le Verre Volé managing partner Thomas Vicente. “Normally it happens naturally, in the course of discussing wine. The right client asks to see the cellar, we give them a tour and it’s there where we offer the little gems hidden in the corners.”

Of course, wine lovers have always sought rarity as an end in itself. Cherry picking is old as vinyl hunting or book collecting. Paul Wasserman, who, with his mother Becky Wasserman, runs pioneering Burgundy import company Le Serbet, puts current trends in perspective: “Until about a decade ago, Burgundy was the bad boy of wine, and Burgundy aficionados were the rebels. Now the bad boy of wine is Natural Wine.”

Meanwhile, at the Left Bank’s historic Café de la Nouvelle Mairie there is a generous list of natural wines—but it’s only shown on demand. In my experience, staff members I don’t know typically point me to the blackboard of glass-pour wines when I request the list. Each time I must insist that there is indeed a wine list—often making a silly rectangular motion in the air with my fingers—before the server concedes and hands it over.

One can’t help wondering: When did restaurants get so coy? And should the best wines necessarily be hidden from clients?

“The market has changed recently,” says Solenne Jouan, wine director at 11ème arrondissement restaurant Le Six Paul Bert. “The high demand for artisan and natural wines in USA, Scandinavia, Japan, etc.—together with the low supply—has resulted in smaller allocations for everyone.”

Jouan puts most of her stock on her list. But she also plays with cherry pickers’ expectations.

“Nowadays in Paris, a lot of people in the wine trade expect that there are special bottles kept aside,” she says. “So we try to surprise them with unusual bottles that average customers might not appreciate.”

Olivier Camus, co-founder of Le Baratin and owner of nearby Le Chapeau Melon, remembers a time when opening the most famous bottles wasn’t necessarily the point of a meal at a natural wine bistrot. “Everything was more informal [in 1989, shortly after Le Baratin opened]. People came often to the bistrots more to meet each other, chat, learn. We didn’t all drink the same things,” he says.

It’s a sharp contrast to today’s market for natural wine, in which a single tweet about, say, some new cuvées by cult Jura winemaker Jean-François Ganevat is enough to stoke international demand.

“The current context is simply that there is a much higher demand than there is supply,” explains Jules Dressner, of natural wine importer Louis/Dressner Selections, which imports Overnoy to the U.S. He describes the effect of rarity on the natural wine market in music terms: “I’m a huge vinyl head. If I hear there is going to be a one-time-only pressing of 500 copies of a new song I love, you can bet your ass I’m gonna go out of my way to get it,” he says. “I won’t deny that the exclusivity and rarity adds to my enjoyment of owning it.”

Of course, wine lovers have always sought rarity as an end in itself. Cherry picking is old as vinyl hunting or book collecting. Paul Wasserman, who, with his mother Becky Wasserman, runs pioneering Burgundy import company Le Serbet, puts current trends in perspective: “Until about a decade ago, Burgundy was the bad boy of wine, and Burgundy aficionados were the rebels. Now the bad boy of wine is Natural Wine.”

What the two wine genres share is an emphasis on terroir and a relative preponderance of small domaines who resist raising prices in the face of skyrocketing demand. Where they differ is the pace of their adaption to global demand.

Burgundy’s market took centuries to become what it is today. Whereas it’s been a scant four decades since Jules Chauvet, Marcel Lapierre and Jacques Néauport conducted their experiments with biodynamic, sulfur-free Beaujolais, and started a revolution. Natural wine now unites a generation of the world’s most acclaimed restaurants, from Copenhagen’s Noma to Belgium’s In De Wulf to Blanca in New York. In Paris it borders on ubiquity, and its rising global popularity is at odds with both the size of the domains and production practices that render it especially vintage-dependent. With so little of the greatest natural wines to go around, are sommeliers right to be cagey about their inventory?

“I have a lot of bottles not on the list,” says sommelier Pascaline Lepeltier of New York’s recently shuttered natural wine mecca Rouge Tomate. “Certain wines are really sought after, and I don’t want the scarcity to dictate an excessive price on our list. But I also don’t want to sell out in a week by offering them at their real reasonable price, either.”

In Paris, this discretion has devolved, in certain places, into an unpleasant “us versus them” mentality. A meal I had at Le Chateaubriand last year tanked almost immediately, when the sommelier claimed to be out of every back-vintage red wine on his list, only to foist upon us an overpriced young Corbières. Last month, at Chez L’Ami Jean, chef Stéphane Jégo’s tourist-thronged Basque bank buster in the 7ème arrondissement, I had a nice chat with the sommelier after our meal and mentioned that I write about wine.

“Oh, you should have told me earlier,” he replied. “We have so much more in the cellar that’s not on the list…”

I rarely want to perform the complex social dance necessary to prove myself worthy of more interesting wine. It’s why—like many Parisians, I suspect—I continually return to restaurants run by friends. In the same way that wine’s yearly production cycle and aging requirements offer a bulwark against the instant gratification of the contemporary era, the human relationships necessary to obtain the best wines remind us of the limits of transactional society. Sometimes, you just have to put in time.

Rodolphe Paquin disagrees, at least in theory. His restaurant, the aforementioned Repaire de Cartouche, possesses one of Paris’s greatest natural wine cellars. “Is it logical that the most interesting side of an establishment should be reserved for connoisseurs or friends? I find that a little bit egotistical. Here, everything is listed,” he says.

Then he clarifies: “I’ll say just that there are a few private things that aren’t on the list, because they’re mine and I share them with friends. But otherwise what we have is on the list. Everything is there. Except certain bottles.”