More than two dozen restaurants across New Haven are gearing up for one of their busiest weeks of the year.

For Restaurant Week this spring, 27 restaurants — the most in the semi-annual event’s four-year history — are offering discounted, fixed-price menus. Restaurant Week, which is held each year in the fall and spring, kicked off Sunday and will run until Friday, and six local restaurant owners and managers said they are almost fully booked for the week.

“We have grown and grown every year,” said Stacy Royal of the public relations firm Lou Hammond & Associates, who is promoting Restaurant Week. “The event continues to exceed our expectations.”

Participating restaurants are offering special fixed-price, three-course menus, which cost $29.00 for dinner and $16.38 (in honor of the year New Haven was founded) for lunch.

“Reservations are almost a necessity,” said David Foster, chef at Foster’s Restaurant on Orange Street. “We’re already almost filled up.”

At the same time that Restaurant Week diners are being adventurous with their taste buds, chefs too are taking advantage of the opportunity to try out new dishes.

“A lot of us try to introduce new things since you’re getting a new crowd, “ said Dave Allen, supervisor at Bentara Spicy Malaysian Cuisine on Orange Street. “Our business has been doubling every time we do it,” he added.

Some restaurants are offering special menus that include only a few of the dishes on their normal menus. Consiglio’s on Wooster Street, for example, is offering a limited menu with its most popular dishes so that customers can get a feel for the restaurant’s specialties.

But other restaurants pride themselves on the fact that their menus and recipes are not altered for Restaurant Week, allowing them to promote old-time favorites.

“What’s important to us is that we show people what we’re about all the time — nothing special,” said Stephen Majoros, a supervisor at Central Steakhouse on Orange Street. “We don’t cheapen the menu or shrink the portions.”

During last spring’s Restaurant Week, participating restaurants reported 35 to 100 percent increases in the number of reservations from the previous Restaurant Week, Royal said, adding that Restaurant Week brings in an average of 35,000 diners and shoppers to Downtown New Haven.

The first Restaurant Week in New Haven had 18 participants.