NEW YORK » At a pea-size Lower East Side bistro known for its fries, the admonition is spelled out on a chalkboard: No ketchup. At a popular gastropub in the West Village, customers cannot have the burger with any cheese other than Roquefort.

And at Murray’s Bagels in Greenwich Village and Chelsea, the morning crowd can order its bagels topped any number of ways but never — ever! — toasted.

"It’s really annoying, because a toasted bagel is kind of fierce, right?" Jamie Divine, a product designer and frequent patron, said with a hint of an eye-roll.

New York has spawned a breed of hard-line restaurants and cafes that are saying no. No to pouring takeout espressos, or grinding more than a pound of coffee at a time. No to taming the intensity of a magma-spicy dish, or making substitutions of any kind. And most of all, no to the 21st-century conviction that everything can be accessorized to the customer’s taste.

"People just assume that every restaurant should be for everyone — I could understand that if we were in a town with, like, 20 restaurants," said David Chang, whose small empire of Momofuku restaurants is well known for refusing to make substitutions or provide vegetarian options. "Instead of trying to make a menu that’s for everyone, let’s make a menu that works best for what we want to do."

He added, "The customer is not always right."

This coterie of food purists — or puritans, perhaps — is hardly limited to New York. The chef-owner of the Michelin-starred Chicago restaurant Graham Elliot does not serve decaffeinated coffee at his new sandwich shop and coffee bar, Grahamwich, because, Elliot said in an e-mail, "we decided to let our inner purists shine through and showcase coffee for what it is — a flavorful, caffeinated elixir."

Clark Wolf, a restaurant consultant in Manhattan, recalled a San Francisco spot called the Pink Poodle that would not supply salt or pepper because, Wolf said, the chef supposedly seasoned every dish perfectly.

But New York has a hallowed history of persnickety cooks: Kenny Shopsin became something of a cult figure for the litany of rules — including no parties bigger than four, and no more than one order at each table of any particular dish — enforced for years at Shopsin’s diner in the West Village, now a small outpost at the Essex Street Market on the Lower East Side.

Arthur Schwartz, a food writer and historian, recalled a restaurant that New Orleans chef Paul Prudhomme opened in Manhattan more than 20 years ago that also prohibited dining companions from ordering the same dish.

"It didn’t last very long," Schwartz said, "because in those days we all said: ‘Too many rules. New Yorkers are not going to do this."’

Yet in a city filled with newcomers seeking a sense of belonging, rules can be part of the attraction.

"One reason people go to a particular restaurant is they want to feel part of a particular community," Schwartz said — even if that community is based on nothing more than a shared appreciation for carefully tended espresso that never touches a paper cup.

"You’re supposed to drink espresso fast," said Caroline Bell, an owner of Cafe Grumpy, explaining that paper lets the heat dissipate too quickly.

When some customers at the three outposts in Brooklyn and Manhattan became, well, grumpy over the lack of takeout espresso, Bell instituted a new policy, meant to be taken more with a wink than with the snarl of the cafe’s logo: Patrons can get an espresso to go, if they pay $12 to drink it from a porcelain cup they can keep.

"People actually do that," she said. "There’s a guy that comes in every day to Chelsea with that cup and gets espresso."

Some restaurateurs say they limit choices because it allows them to serve items consistently prepared the way they want.

"Cooks are creatures of habit," Chang said. "To do this ‘Can I get this with no olives, can I get the salad chopped, sauce on the side’ — some of those special requests are ridiculous. My personal opinion is that a lot of people say they have a special allergy or they don’t like something so they can get better service."

April Bloomfield, who at the Spotted Pig serves burgers with or without Roquefort but refuses to substitute a different cheese, said too many deviations could simply overwhelm the kitchen.

"I just wanted a good burger that was solid and tasty and consistent," she said.

And at Pepe Rosso in SoHo, said Michele Costa, a partner, there was not enough space to accommodate decaffeinated coffee, skim milk and diet soda along with the regular items.

"If you’re really on a diet, drink water," Costa said, laughing.

A Pepe Rosso branch in Grand Central Terminal allows Diet Coke, he said, but only because the manager does not heed to Costa tells him not to.

Some of these quirks are cultural. At Le Relais de Venise L’Entrecote, a Parisian import in East Midtown that offers a set menu of salad and steak frites, diners are asked a single question: Would you like your meat cooked well, medium, rare or bleu (extra rare). Woe unto those who want it medium rare.

"We have no medium rare in France, and we are copying the French way," said Darin Nathan, a partner in the restaurant, adding that the French rare was a close alternative. (A recent request for guidance from a waitress at a recent lunch elicited only the curt statement, "Rare is red; medium is pink.")

Some restrictions are personal. At Zucco: Le French Diner on Orchard Street, Greko Chemoul and his father, Zucco, who died last year, banned ketchup and Budweiser because they did not seem suitable accompaniments for the establishment’s food.

"If I go to an American restaurant or pub, I have my burger with ketchup," Greko Chemoul said. "But I don’t think it looks good when I have ketchup on the side of my coq au vin or grilled lamb. It’s a question of design."

The diner also discourages customers from participating in the Zagat guide.

For some customers, the rules seem to elevate the blood pressure or inspire subterfuge.

At Cafe Grumpy in Park Slope, Benjamin Anastas, a writer, said the counterman had refused to grind two pounds of espresso beans at once, expressing concern that the coffee would lose its freshness before Anastas could brew it. The solution?

"I told him I was going to drink it all over the weekend," Anastas said.

Other patrons are left bewildered. Despite the no-toasting policy at Murray’s Bagels, afternoon customers can order a pizza bagel that is warmed in the oven. (That could inspire a new version of Jack Nicholson’s on-the-edge customer in "Five Easy Pieces," as in: "I’d like a toasted pizza bagel with butter. Hold the cheese. Hold the tomato sauce.")

Divine has given up trying to get a toasted bagel at Murray’s.

"I still have yet to understand why a not-toasted bagel is culinarily better than another bagel," he said.

Banning condiments, however, was just fine by him.

"Don’t get him started on mayonnaise," said his friend Daniel Bender, a student at Parsons the New School for Design, as Divine pronounced: "Condiments are weird."